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The point we have next to determine is how we can utilise the properties of reflection for the purposes of astronomical observation. Many admirable plans have been suggested. The first that was put on paper was made by Gregory, who pointed out that if we had a concave mirror, we should get from this mirror an image of the object viewed at the focus in front of it, as in Fig. 51. Of course we cannot at once utilise this focal image by using an eyepiece in the same way as we do in a refractor, because the observer’s head would stop the light, and the mirror would be useless, and all the suggestions which have been made, have reference to obtaining the image in such a position that we are able to view it conveniently.

Gregory, the Scottish astronomer above referred to, in 1663 suggested a method, and it has turned out to be a good one, of utilizing reflection by placing a small mirror D C, Fig. 54, on the other side of the focus A of the large one, at such a distance that the image at A is again focussed at B by reflection from the small mirror; and at B we get of course an enlarged image of A. The rays of light proceeding to B would, however, be intercepted by the large mirror, unless an aperture were made in the large mirror of the size of the small one through which the rays could pass and be rendered parallel by means of an eyepiece placed just behind the large mirror. So that towards the object is the small mirror C, and there is an eyepiece E, which enables the image of the object to be viewed after two reflections, first from the large mirror and then from the small one. Mr. Short (who made the best telescopes of this construction, and did much for the optical science of the last century) altered the position of the small mirror with reference to the focus of the large one, by sliding it along the tube by a screw arrangement, F, and so was enabled to focus both near and distant objects without altering the eyepiece.

Fig. 54.—Reflecting Telescope (Gregorian).

But before this was put into practice, Sir Isaac Newton (in 1666) made telescopes on a totally different plan.

The eyepiece of the Newtonian telescope is at the side of the tube, and not at the end, as in Gregory’s. We have next to inquire how this arrangement is carried out, and, like most things, it is perfectly simple when one knows how it is done. There is a large mirror at the bottom of the tube as in the Gregorian, but not perforated, and the focus of the mirror would be somewhere just in front of the end of the tube. Now in this case we do not allow the beam to get to the focus at all in the tube or in front of it; but before it comes to the focus it is received on a small diagonal plane surface m, and thus it is at once thrown outwards at right angles through the side of the tube, and comes to a focus in front of an eyepiece, placed at the side, ready to be viewed the same as an image from a refractor (Fig. 55).

Fig. 55.—Newton’s Telescope.

The next arrangement is one which Mr. Grubb has recently rescued from obscurity, and it is called the Cassegrainian form. It will be seen on referring to that, Fig. 56, if the small mirror, C, were removed, the rays from the mirror A B would come to a focus at F.

In the Gregorian construction a concave reflector was used outside that focus (at C, Fig. 54), but Cassegrain suggested that if, instead of using a concave reflector outside the focus, a reflector with a convex surface were placed inside it, we should arrive at very nearly the same result, provided we retain the hole in the large mirror. The converging rays from A B will fall on the convex surface of the mirror C, which is of such a curvature and at such a distance from F, the focus of the large mirror, that the rays are rendered less converging, and do not come to a focus until they reach D, where an image is formed ready to be viewed by the eyepiece E. It appears from this, that the convex mirror is in this case acting somewhat in the same manner as the concave lens does in the Galilean telescope.

Fig. 56.—Reflecting Telescope (Cassegrain).

Fig. 57.—Front View Telescope (Herschel).

Then, lastly, we have the suggestion which Sir William Herschel soon turned into more than a suggestion. The mirror M in this arrangement is placed at the bottom of the tube as in the other forms, but, instead of being placed flat on the bottom it is slightly tipped, so that if the eyepiece is placed at the edge of the extremity of the tube all parallel rays falling on the mirror are reflected to the side of the tube at the top where the eyepiece is, instead of being reflected to a convex or other mirror in the middle.

This is called the front view telescope, and it enabled Sir William Herschel to make his discoveries with the forty-feet reflector. With small telescopes this form could not be adopted, as the observer’s head would cover some part of the tube and obstruct the light, but with large telescopes the amount of light stopped by the head is small in proportion to what would be lost by using a small mirror.

These are in the main the four methods of arranging reflecting telescopes—the Gregorian, the Cassegrainian, the Newtonian, and the Herschelian.

In order to make large reflectors perfect—large telescopes of short focus, because that is one of the requirements of the modern astronomer—we have to battle against spherical aberration.

We have already seen that the power of substances to refract light differs for different colours, and we have seen the varied refraction of different parts of the spectrum, and the necessity of making lenses achromatic. Now there is one enormous advantage in favour of the reflector. We do not take our light to bits and put it together again as with an achromatic lens. But curiously enough, there is a something else which quite lowers the position of the reflector with regard to the refractor. Although, in the main all the light falling in parallel lines on a concave surface is reflected to a focus, this is only true in a general sense, because, if we consider it, we find an error which increases very rapidly as the diameter of the mirror increases or as the focal length diminishes. For instance, D I, Fig. 58, is the segment of a circle, or the section of a sphere—if we deal with a solid figure. D C, E G and H I, are three lines representing parallel rays falling on different parts of it. According to that law which we have considered, we can find where the ray E G will fall. We draw a line L, G, from the centre to the point of reflection, and make the angle F G L, equal to the angle of incidence E G L; then F will be the focus, so far as this part of the mirror is concerned. Now let us repeat the process for the ray H I, and we shall find that it will be reflected to K, a point nearer the mirror than F, and it will be seen that the further the rays are from the axis D C, the further from the point F is the light reflected; so that if we consider rays falling from all parts of the reflecting surface, a not very large but a distinctly visible surface is covered with light, so that a spherical surface will not bring all the rays exactly to a point, and with a spherical mirror we shall get a blurred image. We can compare this imperfection of the reflector, called spherical aberration, with the chromatic aberration of the object-glass.

Fig. 58.—Diagram Illustrating Spherical Aberration.

Fig. 59.—Diagram Showing the Proper Form of Reflector to be an Ellipse.

Newton early calculated the ratio of imperfection depending upon these properties of light, first of dispersion and then of spherical aberration, and he found that in the refracting telescope the chromatic aberration was more difficult to correct and get rid of than the spherical aberration of the reflector, so that in Newton’s time, before achromatic lenses were constructed, the reflector with its aberration had the advantage. It must now be explained how this difficulty is got over. What is required to produce a mirror capable of being used for astronomical purposes, is to throw back the edges of the mirror to the dotted line A C I, Fig. 58, which will make the margin of the mirror a part of a less concave mirror, and so its focus will be thrown further from itself—to F, instead of to K. Now let us consider what curve this is, that will throw all the rays to one point. It is an ellipse, as will be seen by reference to Fig. 59, in which, instead of having a spherical surface the section of which is a circle, we deal with a surface whose section is an ellipse.

It will be seen in a moment, that by the construction of an ellipse any light coming in any direction from the point A, which represents one of the foci of the curve, must necessarily be reflected back to the other focus, B, of the curve, for it is a well-known property of this curve that the angles made with a tangent C D, by lines from the foci are equal; and the same holds good for the angles made at all other tangents; and it will be seen at once that this is better than a circular curve, because by making the distance between the foci almost infinite we shall have the star or object viewed at one focus and its image at the other; if we use any portion of the reflecting surface we shall still get the rays reflected to one point only. It must also be noticed, that unless we have an ellipse so large that one focus shall represent the sun or a particular star we want to look at, this curve will not help us in bringing the light to one point, but if we use the curve called the parabola, which is practically an ellipse with one focus at an infinite distance, we do get the means of bringing all the rays from a distant object to a point. Hence the reflector, especially when of large diameter, is of no use for astronomical purposes without the parabolic curve.

That it is extremely difficult to give this figure may be gathered from Sir John Herschel’s statement, that in the case of a reflecting telescope, the mirror of which is forty-eight inches in diameter and the focal distance of which is forty feet, the distance between the parabolic and the spherical surface, at the edges of the mirror, will be represented by something less than a twenty-one thousandth part of an inch, or, more accurately, 1 21333 inch. In Fig. 58 the point A represents the extreme edge of the curve of the parabolic mirror, and D that of the circular surface before altered into a parabola.

At the time of Sir William Herschel the practical difficulties in constructing large achromatic lenses led to the adoption by him of reflectors beginning with small apertures of six inches to a foot, and increasing till he obtained one of four feet in diameter and forty-six feet focal length. This has been surpassed by Lord Rosse, whose well-known telescope is six feet diameter, and fifty-three feet focal length. Mr. Lassell, Mr. De La Rue, M. Foucault and Mr. Grubb, have also more recently succeeded in bringing reflectors to great perfection.

How the work has been done will be fully stated in the sequel.