than this: to measure an
angle about equal to that subtended by a halfpenny 2,000 feet from the
eye, within a little more than a thousandth part of its value.

The angle thus represented is what is called the "horizontal parallax"
of the sun. By this amount--the breadth of a halfpenny at 2,000 feet--he
is, to a spectator on the rotating earth, removed at rising and setting
from his meridian place in the heavens. Such, in other terms, would be
the magnitude of the terrestrial radius as viewed from the sun. If we
knew this magnitude with certainty and precision, we should also know
with certainty and precision--the dimensions of the earth being, as they
are, well ascertained--the distance of the sun. In fact, the one
quantity commonly stands for the other in works treating professedly of
astronomy. But this angle of parallax or apparent displacement cannot be
directly measured--cannot even be perceived with the finest instruments.
Not from its smallness. The parallactic shift of the nearest of the
stars as seen from opposite sides of the earth's orbit, is many times
smaller. But at the sun's limb, and close to the horizon, where the
visual angle in question opens out to its full extent, atmospheric
troubles become overwhelming, and altogether swamp the far more minute
effects of parallax.

There remain indirect methods. Astronomers are well acquainted with the
proportions which the various planetary orbits bear to each other. They
are so connected, in the manner expressed by Kepler's Third Law, that
the periods being known, it only needs to find the interval between any
two of them in order to infer at once the distances separating them all
from one another and from the sun. The plan is given; what we want to
discover is the scale upon which it is drawn; so that, if we can get a
reliable measure of the distance of a single planet from the earth, our
problem is solved.

Now some of our fellow-travellers in our unending journey round the sun,
come at times well within the scope of celestial trigonometry. The orbit
of Mars lies at one point not more than thirty-five million miles
outside that of the earth, and when the two bodies happen to arrive
together in or near the favourable spot--a conjuncture which occurs
every fifteen years--the desired opportunity is granted. Mars is then
"in opposition," or on the _opposite_ side of us from the sun, crossing
the meridian consequently at midnight.[749] It was from an opposition o