the position of the tube accordingly.

The best tests for determining the defining power of a telescope are
close double or multiple stars, the components of which are not very
unequal. The illuminating power should be tested by directing the
telescope towards double or multiple stars having one or more minute
components. Many of the nebulæ serve as tests both for illumination and
defining power. As we proceed we shall meet with proper objects for
testing different telescopes. For the present, let the following list
suffice. It is selected from Admiral Smyth's tests, obtained by
diminishing the aperture of a 6-in. telescope having a focal length of
8-1/2 feet:

A two-inch aperture, with powers of from 60 to 100, should exhibit

[alpha] Piscium (3"·5). | [delta] Cassiopeiæ (9"·5),
| mag. (4 and 7-1/2)
[gamma] Leonis (3"·2). | Polaris (18"·6), mag. (2-1/2
| and 9-1/2)

A four-inch, powers 80 to 120, should exhibit

[xi] Ursæ Majoris (2"·4). | [sigma] Cassiopeiæ (3"·1),
| mag. (6 and 8).
[gamma] Ceti (2"·6). | [delta] Geminorum (7"·1),
| mag. (4 and 9).

The tests in the first column are for definition, those in the second
for illumination. It will be noticed that, though in the case of Polaris
the smaller aperture may be expected to show the small star of less than