To determine whether the spherical aberration is corrected, the telescope should be directed towards a star of the third or fourth magnitude, and focussed for distinct vision. A cap with an aperture of about one-half its diameter should then be placed over the object-glass. If no new adjustment is required for distinct vision, the spherical aberration is corrected, since the mean focal length and the focal length of the central rays are equal. If, when the cap is on, the eye-piece has to be pulled out for distinct vision, the spherical aberration has not been fully corrected; if the eye-piece has to be pushed in, the aberration has been over-corrected. As a further test, we may cut off the central rays, by means of a circular card covering the middle of the object-glass, and compare the focal length for distinct vision with the focal length when the cap is applied. The extent of the spherical aberration may be thus determined; but if the first experiment gives a satisfactory result, no other is required. A star of the first magnitude should next be brought into the field of view. If an irradiation from one side is perceived, part of the object-glass has not the same refractive power as the rest; and the part which is defective can be determined by applying in different positions a cap which hides half the object-glass. If the irradiation is double, it will probably be found that the object-glass has been too tightly screwed, and the defect will disappear when the glass is freed from such undue pressure. If the object-glass is not quite at right angles to the axis of the tube, or if the eye-tube is at all inclined, a like irradiation will appear when a bright star is in the field. The former defect is not easily detected or remedied; nor is it commonly met with in the work of a careful optician. The latter defect may be detected by cutting out three circular cards of suitable size with a small aperture at the centre of each, and inserting one at each end of the eye-tube, and one over the object-glass. If the tube is rightly placed the apertures will of course lie in a right line, so that it will be possible to look through all three at once. If not, it will be easy to determine towards what part of the object-glass the eye-tube is directed, and to correct 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 nebulae 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: