In other words, the closest double star which a telescope will separate, expressed in seconds of arc, equals four and a half divided by the diameter of the aperture of the object-glass in inches.
A 412-inch object-glass will separate the components of a double star when they are within one second of each other; a 9-inch object-glass when within half a second of each other, and a 30-inch object-glass when within about one seventh of a second of each other.
Diagram 8 shows the advantage of increasing the aperture of the
Diagram 8.
object-glass; it represents the triple star γ Andromedæ as seen through a 412-inch, 9-inch, and 30-inch object-glass, in all cases with a one-sixth-of-an-inch eye-piece, which makes the diffraction disks plainly visible, and in every case of the same apparent size but of a brilliancy proportionate to the area of the corresponding object-glass. Through the 412-inch the upper star can not be separated into two, through the 9-inch, however, both components are distinctly visible, while through the 30-inch they appear widely separated.
If the one-sixth-of-an-inch eye-piece were replaced by another whose focal length was only one twelfth of an inch, the apparent distance between the centers of the stars would of course be twice as great, but the diameter of the diffraction disks would also be twice as large, and therefore have but one fourth their former brightness, and the close double star, instead of being seen to better advantage, would merely appear as two larger and much fainter disks than before, and could not be divided so well.
A very good way to see the effect of using a power high enough
