diameter by its passage through the object-glass and eye-piece to a cylinder of light small enough entirely to enter the eye.
When, however, this condition is fulfilled, it is clear that, when the eye receives the light from a luminous point through such a telescope, that point must appear as much brighter than it would if viewed directly, with the telescope out of the way, as the area of the object-glass exceeds the area of the pupil of the eye.
Bearing in mind the properties of similar triangles, it is also plain from Diagram 6 that the diameter of the cylinder of light-waves emerging from the eye-piece is as much less than the diameter of the cylinder of light-waves entering the object-glass as the focal length of the eye-piece is less than the focal length of the object-glass. As the focal lengths of object-glasses never vary much from thirteen times their diameter, the focal length of the eye-piece must be thirteen times the diameter of the emerging cylinder of light-waves, which, as just stated, should never exceed in diameter that of the pupil of the eye. Hence the focal length of the eye piece should never exceed thirteen times one fifth of an inch, or about two and a half inches. This is the greatest focal length which an eye-piece can have to utilize the whole aperture of such an object-glass; to use an eye-piece of greater focal length admits to the eye light only from the central part of the object-glass, and stars appear fainter through it than they do through an eye-piece whose focal length is equal to, or less than, two and a half inches.
As already stated, the vibrating molecule, the center of the lens, and the focus of the converging spherical wave-fronts emerging from it, lie in a straight line.
Diagram 7 represents, with center lines only, to avoid confusion,
the light from an infinitely distant vibrating molecule, situated at an angular distance α from the direction of the axis of the telescope, passing through the object-glass and eye-piece. On emerging from the eye-piece the light will be traveling in a direction whose inclination to the axis of the telescope is equal to the angle β.
The actual angular distance of the luminous point from the axis of