implies) an instrument to render distant objects visible, must be both a magnifying and an illuminating instrument.

Fig. 1.

Let EF, fig. 1, be an object, not near to AB as in the figure, but so far off that the bounding lines from A and B would meet at the point corresponding to the point P. Then if a large convex glass AB (called an object-glass) be interposed between the object and the eye, all those rays which, proceeding from P, fall on AB, will be caused to converge nearly to a point p. The same is true for every point of the object EMF, and thus a small image, emf, will be formed. This image will not lie exactly on a flat surface, but will be curved about the point midway between A and B as a centre. Now if the lens AB is removed, and an eye is placed at m to view the distant object EMF, those rays only from each point of the object which fall on the pupil of the eye (whose diameter is about equal to mp suppose) will serve to render the object visible. On the other hand, every point of the image emf has received the whole of the light gathered up by the large glass AB. If then we can only make this light available, it is clear that we shall have acquired a large increase of light from the distant object. Now it will be noticed that the light which has converged to p, diverges from p so that an eye, placed that this diverging pencil of rays may fall upon it, would be too small to receive the whole of the pencil. Or, if it did receive the whole of this pencil, it clearly could not receive the whole of the pencils proceeding from other parts of the image emf. Something would be gained, though, even in this case, since it is clear that an eye thus placed at a distance of ten inches from emf (which is about the average distance of distinct vision) would not only receive much more light from the image emf, than it would from the object EMF, but see the image much larger than the object. It is in this way that a simple object-glass forms a telescope, a circumstance we shall presently have to notice more at length. But we want to gain the full benefit of the light which has been gathered up for us by our object-glass. We therefore interpose a small convex glass ab (called an eye-glass) between the image and the eye, at such a distance from the image that the divergent pencil of rays is converted into a pencil of parallel or nearly parallel rays. Call this an emergent pencil. Then all the emergent pencils now converge to a point on the axial line m M (produced beyond m), and an eye suitably placed can take in all of them at once. Thus the whole, or a large part, of the image is seen at once. But the image is seen inverted as shown. This is the Telescope, as it was first discovered, and such an arrangement would now be called a simple astronomical Telescope.

Let us clearly understand what each part of the astronomical telescope does for us:—

The object-glass AB gives us an illuminated image, the amount of illumination depending on the size of the object-glass. The eye-glass enables us to examine the image microscopically.

We may apply eye-glasses of different focal length. It is clear that the shorter the focal length of ab, the nearer must ab be placed to the image, and the smaller will the emergent pencils be, but the greater the magnifying power of the eye-glass. If the emergent pencils are severally larger than the pupil of the eye, light is wasted at the expense of magnifying power. Therefore the eye-glass should never be of greater focal length than that which makes the emergent pencils about equal in diameter to the pupil of the eye. On the other hand, the eye-glass must not be of such small focal length that the image appears indistinct and contorted, or dull for want of light.

Fig. 2.

Let us compare with the arrangement exhibited in fig. 1 that adopted by Galileo. Surprise is sometimes expressed that this instrument, which in the hands of the great Florentine astronomer effected so much, should now be known as the non-astronomical Telescope. I think this will be readily understood when we compare the two arrangements.

In the Galilean Telescope a small concave eye-glass, ab (fig. 2), is placed between the object-glass and the image. In fact, no image is allowed to be formed in this arrangement, but the convergent pencils are intercepted by the concave eye-glass, and converted into parallel emergent pencils. Now in fig. 2 the concave eye-glass is so placed as to receive only a part of the convergent pencil A p B, and this is the arrangement usually adopted. By using a concave glass of shorter focus, which would therefore be placed nearer to m p, the whole of the convergent pencil might be received in this as in the former case. But then the axis of the emergent pencil, instead of returning (as we see it in fig. 1) towards the axis of the telescope, would depart as much from that axis. Thus there would be no point on the axis at which the eye could be so placed as to receive emergent pencils showing any considerable part of the object. The difference may be compared to that between looking through the small end of a cone-shaped roll of paper and looking through the large end; in the former case the eye sees at once all that is to be seen through the roll (supposed fixed in position), in the latter the eye may be moved about so as to command the same range of view, but at any instant sees over a much smaller range.

To return to the arrangement actually employed, which is illustrated by the common opera-glass. We see that the full illuminating power of the telescope is not brought into play. But this is not the only objection to the Galilean Telescope. It is obvious that if the part C D of the object-glass were covered, the point P would not be visible, whereas, in the astronomical arrangement no other effect is produced on the visibility of an object, by covering part of the object-glass, than a small loss of illumination. In other words, the dimensions of the field of view of a Galilean Telescope depend on the size of the object-glass, whereas in the astronomical Telescope the field of view is independent of the size of the object-glass. The difference may be readily tested. If we direct an opera-glass upon any object, we shall find that any covering placed over a part of the object-glass becomes visible when we