A second of arc corresponds to the size of an object at a distance of
206,265 times its diameter; to a millimeter seen at 206 meters'
distance; to a hair, 1/10 of a millimeter in thickness, at 20 meters'
distance (more invisible to the naked eye). And yet this value is in
excess of those actually obtained. In fact:--the apparent displacement
of the nearest star is calculated at 75/100 of a second (0.75"), _i.e._,
from this star, [alpha] of Centaur, the half-diameter of the terrestrial
orbit is reduced to this infinitesimal dimension. Now in order that the
length of any straight line seen from the front be reduced until it
appear to subtend no more than an angle of 0.75", it must be removed to
a distance 275,000 times its length. As the radius of the terrestrial
orbit is 149,000,000 kilometers (93,000,000 miles), the distance which
separates [alpha] of Centaur from our world must therefore =
41,000,000,000,000 kilometers (25,000,000,000,000 miles). And that is
the nearest star. We saw in Chapter II that it shines in the southern
hemisphere. The next, and one that can be seen in our latitudes, is 61
of Cygnus, which floats in the Heavens 68,000,000,000,000 kilometers
(42,000,000,000,000 miles) from here. This little star, of fifth
magnitude, was the first of which the distance was determined (by
Bessel, 1837-1840).
All the rest are much more remote, and the procession is extended to
infinity.
We can not conceive directly of such distances, and in order to imagine
them we must again measure space by time.
In order to cover the distance that separates us from our neighbor,
[alpha] of Centaur, _light_, the most rapid of all couriers, takes 4
years, 128 days. If we would follow it, we must not jump from start to
finish, for that would not give us the faintest idea of the distance: we
must take the trouble to think out the direct advance of the ray of
light, and associate ourselves with its progress. We must see it
traverse 300,000 kilometers (186,000 miles) during the first second of
the journey; then 300,000 more in the second, which makes 600,000
kilometers; then once more 300,000 kilometers during the third, and so
on without stopping for four years and four months. If we take this
trouble we may realize the value of the figure; otherwise, as this
number surpasses all that we are in the habit of realizing, it will have
no significance for us, and will be a dead letter.
If some appalling explosion occurred in this star, and the sound in its
flight of 340 meters (1,115 feet) per second were able to cross the
void that separates us from it, the noise of this explosion would only
reach us in 3,000,000 years.
A train started at a speed of 106 kilometers (65 miles) per hour would
have to run for 46,000,000 years, in order to reach this star, our
neighbor in the celestial kingdom.
The distance of some thirty of the stars has been determined, but the
results are dubious.