c, or the
instant of its entry upon or exit from it. And the differences in these
times (which, owing to the comparative nearness of Venus, are quite
considerable), as observed from remote parts of the earth, can be
translated into differences of space--that is, into apparent or
parallactic displacements, whereby the distance of Venus becomes known,
and thence, by a simple sum in proportion, the distance of the sun. But
in that word "exactly" what snares and pitfalls lie hid! It is so easy
to think and to say; so indefinitely hard to realise. The astronomers of
the eighteenth century were full of hope and zeal. They confidently
expected to attain, through the double opportunity offered them, to
something like a permanent settlement of the statistics of our system.
They were grievously disappointed. The uncertainty as to the sun's
distance, which they had counted upon reducing to a few hundred thousand
miles, remained at many millions.

In 1822, however, Encke, then director of the Seeberg Observatory near
Gotha, undertook to bring order out of the confusion of discordant, and
discordantly interpreted observations. His combined result for both
transits (1761 and 1769) was published in 1824,[752] and met universal
acquiescence. The parallax of the sun thereby established was 8.5776",
corresponding to a mean distance[753] of 95-1/4 million miles. Yet this
abolition of doubt was far from being so satisfactory as it seemed.
Serenity on the point lasted exactly thirty years. It was disturbed in
1854 by Hansen's announcement[754] that the observed motions of the moon
could be drawn into accord with theory only on the terms of bringing the
sun considerably nearer to us than he was supposed to be.

Dr. Matthew Stewart, professor of mathematics in the University of
Edinburgh, had made a futile attempt in 1763 to deduce the sun's
distance from his disturbing power over our satellite.[755] Tobias Mayer
of Gottingen, however, whose short career was fruitful of suggestions,
struck out the right way to the same end; and Laplace, in the seventh
book of the _Mecanique Celeste_,[756] gave a solar parallax derived from
the lunar "parallactic inequality" substantially identical with that
issuing from Encke's subsequent discussion of the eighteenth-century
transits. Thus, two wholly independent methods--the trigonometrical,
or method by survey, and the gravitational, or method by
perturbation--seemed to corroborate each the upshot of the u