The course of a slightly oblique pencil through either eye-piece is exhibited in the figures. The lenses are usually plano-convex, the convexities being turned towards the object-glass in the negative eye-piece, and towards each other in the positive eye-piece. Coddington has shown, however, that the best forms for the lenses of the negative eye-piece are those shown in [fig. 5].
The negative eye-piece, being achromatic, is commonly employed in all observations requiring distinct vision only. But as it is clearly unfit for observations requiring micrometrical measurement, or reference to fixed lines at the focus of the object-glass, the positive eye-piece is used for these purposes.
For observing objects at great elevations the diagonal eye-tube is often convenient. Its construction is shown in [fig. 7]. ABC is a totally reflecting prism of glass. The rays from the object-glass fall on the face AB, are totally reflected on the face BC, and emerge through the face AC. In using this eye-piece, it must be remembered that it lengthens the sliding eye-tube, which must therefore be thrust further in, or the object will not be seen in focus. There is an arrangement by which the change of direction is made to take place between the two glasses of the eye-piece. With this arrangement (known as the diagonal eye-piece) no adjustment of the eye-tube is required. However, for amateurs' telescopes the more convenient arrangement is the diagonal eye-tube, since it enables the observer to apply any eye-piece he chooses, just as with the simple sliding eye-tube.
We come next to the important question of the mounting of our telescope.
The best known, and, in some respects, the simplest method of mounting a telescope for general observation is that known as the altitude-and-azimuth mounting. In this method the telescope is pointed towards an object by two motions,—one giving the tube the required altitude (or elevation), the other giving it the required azimuth (or direction as respects the compass points).
For small alt-azimuths the ordinary pillar-and-claw stand is sufficiently steady. For larger instruments other arrangements are needed, both to give the telescope steadiness, and to supply slow movements in altitude and azimuth. The student will find no difficulty in understanding the arrangement of sliding-tubes and rack-work commonly adopted. This arrangement seems to me to be in many respects defective, however. The slow movement in altitude is not uniform, but varies in effect according to the elevation of the object observed. It is also limited in range; and quite a little series of operations has to be gone through when it is required to direct the telescope towards a new quarter of the heavens. However expert the observer may become by practice in effecting these operations, they necessarily take up some time (performed as they must be in the dark, or by the light of a small lantern), and during this time it often happens that a favourable opportunity for observation is lost.