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
s