to make the diffraction disks obtrusively large is to point the telescope at a rough stone building in very strong sunlight. The small crystalline surfaces in the stone reflect the sun in little shining points of light, which, observed through the telescope, make the building appear as if stuck all over with silver dollars, while an unnatural glassy blurring of the whole image is very apparent. If the illumination will bear it, this appearance can be greatly exaggerated by covering the object-glass with a pasteboard diaphragm in such a manner as to considerably reduce its clear aperture.
For exactly the same reason, a similar blurred appearance is disagreeably noticeable when objects like the Moon or Jupiter are observed with an extremely high power.
From what has just been said, it is obvious that a power higher than that due to a one-sixth-of-an-inch eye-piece is of very little use in connection with an object-glass whose focal length is about thirteen times its clear aperture; but, had the waves of light been created more minute than they are, it would have been possible to employ with advantage a still higher power.
It is thus seen that the focal lengths of telescopic eye-pieces, no matter what the size of the object-glass may be, should all lie between the very narrow limits of two and a half inches for the lowest power and one sixth of an inch for the highest power; six or seven of them give a sufficient range of magnifying power to fully utilize the object-glass of any telescope.
A convenient way of expressing the limiting magnifying powers of a telescope in terms of the size of its object-glass, independently of its ratio of aperture to focal length, is easily deduced from the above by a simple proportion, and is as follows: a telescope will not bear with advantage a lower magnifying power than five nor a higher magnifying power than seventy-five for every inch of clear aperture of its object-glass.
In all that has gone before, we have confined ourselves to the consideration of the single set of light-waves originated by a single vibrating molecule, and to single-convex lenses, having surfaces of the proper curvature, to convert the convex spherical or plane wave-fronts into concave spherical wave-fronts; but how is it in reality?
We have seen that the light of the sun originates in clouds of precipitated carbon from the great upward currents of metallic vapors rising from its interior. It can be demonstrated that the molecules of water are so small that, were one drop enlarged to the size of the earth, the individual molecule would only come up to the size of horse-chestnuts. There is no reason to think that carbon-molecules differ greatly from this in size. Therefore we receive from the sun the enormous number of light-waves originated by each vibrating molecule, suspended through a depth of many miles in the transparent vapors at the surface of a globe 885,000 miles in diameter. These light-waves
