position of the observers remaining the same.
For instance, if the flag-staff were brought
forward to the cross-bar of the A, the angle it
would then form, with the observers at the feet,
would be considerably greater than when it
stood at the top of the letter. On the other
hand, suppose the flag-staff removed to a great
distance—say half a mile away—the angle, or
parallax, would be enormously diminished,
tapering almost to a needle's point.

When we have the whole Earth as our place
of observation instead of a small ten-acre
enclosure, and the heavenly bodies for objects instead
of flag-staffs or trees, the scale is altered, but
not the truth of the facts. Throughout the
universe, all is relative. As on the Earth's
surface objects may be so distant that their parallax
for neighbouring observers is excessively
small; so do there exist in open space visible
objects removed from us by such enormous
intervals that their parallax, seen, not only
from any part of the Earth, but from any part
of the Earth's orbit, is imperceptible. The fixed
stars have no parallax for us. The dog star
alone, the nearest and the brightest of them, is
said to have a parallax, though of extremest
smallness.

Of course it is only when parallax is perceptible
that it can be made to serve as a measure
of distance; and, unfortunately, the smaller it
is, the greater is the difficulty of calculating it
exactly. The parallax of some of the planets,
in certain parts of their orbits, is quite
appreciable. Mars, when on the same side of the
Sun with ourselves and seen by observers placed
at distant spots on the earth, say Paris and
Cayenne, appears at the same moment to
occupy different positions in the sky. The
Sun, more distant, has a much smaller parallax,
which is consequently more difficult of
determination.

During every one of our waking hours, our
unassisted eyes are continually noting the parallax
of surrounding objects, without our having
studied astronomy, and without our even being
aware of it. We are trigonometricians in spite
of ourselves. We unconsciously solve problems
which, on a larger scale, mathematicians are
proud to work out with much mental labour.
Observe that I have written "eyes," in the
plural, because a single eye cannot do the same
thing.

This unsuspected, every-day process is one of
the means by which we judge of distance:

You. are comfortably sitting by the fire in
your parlour; on the window-sill is a geranium
in leaf; on the opposite side of the street or
square is a house which probably has windows.
Shut one eye, and bring one leaf of the geranium
in exact line with one of the windows of the
opposite house. Then, without stirring a hair's
breadth if you can help it, open the closed eye
and shut the open one. The leaf will no longer
be in line with the distant window. Seen from
a different point of view, it will be in line with
something else. It is the combination of what
is seen by each eye separately which gives their
relief and their perspective to the flat pictures
seen in a stereoscope—an optical toy which is
useless to a one-eyed man.

As the geranium leaf appears to each of our
eyes separately to occupy a different position
with reference to the window on the opposite
side of the street, so does Venus, while making
her transit across the Sun, appear to two
distant observers on the surface of the Earth to
occupy a different position with reference to the
Sun. The marvel is that, from these apparently
different positions, mathematicians should have
deduced, with a wonderful approach to perfect
precision, the enormous distance from the Earth
to the Sun.

The admirable idea of calculating the Sun's
parallax from observations of the transits of
Venus is due to Halley. In 1678, while,
still quite young, he was observing, in the
Island of St. Helena, the stars surrounding
the South Pole of the heavens (which, conse-
quently, are invisible to us), when, happening
to observe a passage of Mercury across the
Sun, he was struck with the exactitude resulting
from the observation of the beginning and
the end of the phenomenon—the consequence
of the formation or the rupture of a tiny thread
of light between the disk of the planet and
that of the Sun at the precise moment of the
interior contact of the two disks. He
immediately comprehended that from this class of
observations the parallax of the Sun might
be accurately deduced. But for that
purpose he also saw it was very desirable that
the intervening planet should be further away
from the Sun than Mercury is, and nearer
to the Earth. Venus satisfies this condition.
He therefore worked out his original idea,
applying it to the transits of Venus for
determining the parallax of the Sun with a very
close approximation to the truth, inasmuch
as he believed that the error committed would
not exceed the five-hundredth part of the real
value.

Halley communicated his method to the
world in 1691, in a Memoir which appeared in
the Philosophical Transactions of the Royal
Society of London, No. 193. He afterwards,
in 1716, supplied to No. 348 of the same
publication all the developments necessary to
demonstrate its great importance. He even
gave the instructions for applying his theory to
the next expected transit of Venus, which
would occur in the month of June, 1761. As
Halley was then (1716) sixty years of age, he
could have little hope of witnessing the results
of his own discovery, which promised such
excellent chances of success in determining
the precise distance of the Sun from the
Earth.

In what has been said, the distance from the
Earth to the Sun is spoken of as a determinate,
unchangeable quantity. We know, however,
that that distance is constantly varying from
day to day. The fact may be ascertained with
the greatest facility by measuring the Sun's
diameter at different seasons. This diameter,