The Telescope

by Louis Bell

To sum up Dawes’ results he established the fact that on the average a one inch aperture would enable one to separate two 6th magnitude stars the centers of which were separated by 4.56″. Or, to generalize from this basis, the separating power of any telescope is for very nearly equal stars, moderately bright, 4″.56/A where A is the aperture of the telescope in inches.

Many years of experience have emphasized the usefulness of this approximate rule, but that it is only approximate must be candidly admitted. It is a limit decidedly under that just assigned on the basis of the theory of diffraction for the central bright wave-lengths of the spectrum. Attempts have been made to square the two figures by assuming in the diffraction theory a wave length of 1/55,000 inch, but this figure corresponds to a point well up into the blue, of so low luminosity that it is of no importance whatever in the visual use of a telescope.

The fact is that the visibility of two neighboring bright points as distinct, depends on a complex of physical and physiological factors, the exact relations of which have never been unravelled. To start with we have the principles of diffraction as just explained, which define the relation of the stellar disc to the center of the first dark ring, but we know that under no circumstances can one see the disc out to this limit, since vision fails to take cognizance of the faint rim of the image. The apparent diameter of the diffraction solid therefore corresponds to a section taken some distance above the base, the exact point depending on the sensitiveness of the particular observer’s eye, the actual brilliancy of the center of the disc, and the corresponding factors for the neighboring star.

Fig. 185.—Diffraction Solid for a Disc.

Under favorable circumstances one would not go far amiss in taking the visible diameter of the disc at about half that reckoned to the center of the first dark ring. This figure in fact corresponds to what has been shown to be within the grasp of a good observer under favorable conditions, as we shall presently see.

On the other hand, if the stars are decidedly bright there is increase of apparent diameter of the disc due to the phenomenon known as irradiation, the spreading of light about its true image on the retina which corresponds quite closely to the halation produced by a bright spot on a photographic plate.

If, on the contrary, the stars are very faint the total amount of light available is not sufficient to make contrast over and above the background sufficient to disclose the two points as separate, while if the pair is very unequal the brighter one will produce sufficient glare to quite over-power the light from the smaller one so that the eye misses it entirely.

A striking case of this is found in the companion to Sirius, an extremely difficult object for ordinary telescopes although the distance to the companion is about 10.6″ and its magnitude is 8.4, making a superlatively easy double for the very smallest telescope save for the overpowering effect of the light of the large star. Another notoriously difficult object for small telescopes is δ Cygni, a beautiful double of which the smaller component falls unpleasantly near the first diffraction maximum of the primary in which it is apt to be lost.

“Dawes’ Limit” is therefore subject to many qualifying factors. Lewis, in the papers already referred to (Obs. 37, 378) did an admirable piece of investigation in going through the double star work of about two score trained observers working with telescopes all the way from 4 inches to 36 inches aperture.