parallax and determination of proper motions.

The problem of stellar parallax, simple though it is in its
conception, is the most delicate and difficult of all which the
practical astronomer has to encounter. An idea of it may be gained
by supposing a minute object on a mountain-top, we know not how
many miles away, to be visible through a telescope. The observer
is allowed to change the position of his instrument by two inches,
but no more. He is required to determine the change in the
direction of the object produced by this minute displacement with
accuracy enough to determine the distance of the mountain. This is
quite analogous to the determination of the change in the
direction in which we see a star as the earth, moving through its
vast circuit, passes from one extremity of its orbit to the other.
Representing this motion on such a scale that the distance of our
planet from the sun shall be one inch, we find that the nearest
star, on the same scale, will be more than four miles away, and
scarcely one out of a million will be at a less distance than ten
miles. It is only by the most wonderful perfection both in the
heliometer, the instrument principally used for these measures,
and in methods of observation, that any displacement at all can be
seen even among the nearest stars. The parallaxes of perhaps a
hundred stars have been determined, with greater or less
precision, and a few hundred more may be near enough for
measurement. All the others are immeasurably distant; and it is
only by statistical methods based on their proper motions and
their probable near approach to equality in distribution that any
idea can be gained of their distances.

To form a conception of the stellar system, we must have a unit of