In terrestrial objects, the form, no less than the modes of
illumination, determines the magnitude of the smallest angle of vision
for the naked eye. Adams very correctly observed that a long and
slender staff can be seen at a much greater distance than a square
whose sides are equal to the diameter of the staff. A stripe may be
distinguished at a greater distance than a spot, even when both are of
the same diameter.
The _minimum_ optical visual angle at which terrestrial objects can
be recognised by the naked eye has been gradually estimated lower and
lower, from the time when Robert Hooke fixed it exactly at a full
minute, and Tobias Meyer required 34″ to perceive a black speck on
white paper, to the period of Leuwenhoeck’s experiments with spiders’
threads, which are visible to ordinary sight at an angle of 4″·7. In
Hueck’s most accurate experiments on the problem of the movement of
the crystalline lens, white lines on a black ground were seen at an
angle of 1″·2; a spider’s thread at 0″·6; and a fine glistening wire at
scarcely 0″·2.
Humboldt, when at Chillo, near Quito, where the crests of the
volcano of Pichincha lay at a horizontal distance of 90,000 feet,
was much struck by the circumstance that the Indians standing near
distinguished the figure of Bonpland (then on an expedition to the
volcano), as a white point moving on the black basaltic sides of
the rock, sooner than Humboldt could discover him with a telescope.
Bonpland was enveloped in a white cotton poncho: assuming the
breadth across the shoulders to vary from three to five feet,
according as the mantle clung to the figure or fluttered in the
breeze, and judging from the known distance, the angle at which the
moving object could be distinctly seen varied from 7″ to 12″. White
objects on a black ground are, according to Hueck, distinguished at
a greater distance than black objects on a white ground.
Gauss’s heliotrope light has been seen with the naked eye reflected
from the Brocken on Hobenhagen at a distance of about 227,000 feet,
or more than 42 miles; being frequently visible at points in which
the apparent breadth of a three-inch mirror was only 0″·43.