tieth
part of that of the circle due to aberration; indeed, in the great
majority of cases the parallax of the star is an absolutely insensible
quantity.
There is, however, a still graver and quite insuperable distinction
between the parallactic path and the aberrational path. Let us, for
simplicity, think of a star situated near the pole of the ecliptic, and
thus appearing to revolve annually in a circle, whether we regard either
the phenomenon of parallax or of aberration. As the earth revolves, so
does the star appear to revolve; and thus to each place of the earth in
its orbit corresponds a certain place of the star in its circle. If the
movement arise from annual parallax, it is easy to see where the place
of the star will be for any position of the earth. It is, however, found
that in the movement discovered by Bradley the star never has the
position which parallax assigns to it, but is, in fact, a quarter of the
circumference of its little circle distant therefrom.
A simple rule will find the position of the star due to aberration. Draw
from the centre of the ellipse a radius parallel to the direction in
which the earth is moving at the moment in question, then the extremity
of this radius gives the point on its ellipse where the star is to be
found. Tested at all seasons, and with all stars, this law is found to
be always verified, and by its means we are conducted to the true
explanation of the phenomenon.
We can enunciate the effects of aberration in a somewhat different
manner, which will show even more forcibly how the phenomenon is
connected with the motion of the earth in its orbit. As the earth
pursues its annual course around the sun, its movement at any moment may
be regarded as directed towards a certain point of the ecliptic. From
day to day, and even from hour to hour, the point gradually moves along
the ecliptic, so as to complete the circuit in a year. At each moment,
however, there is always a certain point in the heavens towards which
the earth's motion is directed. It is, in fact, the point on the
celestial sphere towards which the earth would travel continuously if,
at the moment, the attraction of the sun could be annihilated. It is
found that this point is intimately connected with the phenomenon of
aberration. In fact, the aberration is really equivalent to drawing each
star from its mean place towards the Apex of the Earth's Way, as the
point is sometimes termed. It can also be shown
|