In the _Edinburgh Review_, 1850, we find the following illustrations of
the enormous propagation of minute errors:
The rod used in measuring a base-line is commonly about ten
feet long; and the astronomer may be said truly to apply that
very rod to mete the distance of the stars. An error in placing
a fine dot which fixes the length of the rod, amounting to
one-five-thousandth of an inch (the thickness of a single silken
fibre), will amount to an error of 70 feet in the earth’s diameter,
of 316 miles in the sun’s distance, and to 65,200,000 miles in
that of the nearest fixed star. Secondly, as the astronomer in his
observatory has nothing further to do with ascertaining lengths or
distances, except by calculation, his whole skill and artifice are
exhausted in the measurement of angles; for by these alone spaces
inaccessible can be compared. Happily, a ray of light is straight:
were it not so (in celestial spaces at least), there would be an
end of our astronomy. Now an angle of a second (3600 to a degree)
is a subtle thing. It has an apparent breadth utterly invisible to
the unassisted eye, unless accompanied with so intense a splendour
(_e. g._ in the case of a fixed star) as actually to raise by its
effect on the nerve of sight a spurious image having a sensible
breadth. A silkworm’s fibre, such as we have mentioned above,
subtends an angle of a second at 3½ feet distance; a cricket-ball,
2½ inches diameter, must be removed, in order to subtend a second,
to 43,000 feet, or about 8 miles, where it would be utterly
invisible to the sharpest sight aided even by a telescope of some
power. Yet it is on the measure of one single second that the
ascertainment of a sensible parallax in any fixed star depends;
and an error of one-thousandth of that amount (a quantity still
unmeasurable by the most perfect of our instruments) would place
the star too far or too near by 200,000,000,000 miles; a space
which light requires 118 days to travel.