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.

[Illustration:  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.