ounting for all the phenomena of the heavens--should depend upon the
fortuitous circumstance of five times the mean motion of Saturn being
equal to twice the mean motion of Jupiter? The beauty of the conception
and the ultimate result are here equally worthy of admiration.[34]

We have just explained how Laplace demonstrated that the solar system
can experience only small periodic oscillations around a certain mean
state. Let us now see in what way he succeeded in determining the
absolute dimensions of the orbits.

What is the distance of the sun from the earth? No scientific question
has occupied in a greater degree the attention of mankind;
mathematically speaking, nothing is more simple. It suffices, as in
common operations of surveying, to draw visual lines from the two
extremities of a known base to an inaccessible object. The remainder is
a process of elementary calculation. Unfortunately, in the case of the
sun, the distance is great and the bases which can be measured upon the
earth are comparatively very small. In such a case the slightest errors
in the direction of the visual lines exercise an enormous influence upon
the results.

In the beginning of the last century Halley remarked that certain
interpositions of Venus between the earth and the sun, or, to use an
expression applied to such conjunctions, that the _transits_ of the
planet across the sun's disk, would furnish at each observatory an
indirect means of fixing the position of the visual ray very superior in
accuracy to the most perfect direct methods.[35]

Such was the object of the scientific expeditions undertaken in 1761 and
1769, on which occasions France, not to speak of stations in Europe, was
represented at the Isle of Rodrigo by Pingre, at the Isle of St. Domingo
by Fleurin, at California by the Abbe Chappe, at Pondicherry by
Legentil. At the same epochs England sent Maskelyne to St. Helena, Wales
to Hudson's Bay, Mason to the Cape of Good Hope, Captain Cooke to
Otaheite, &c. The observations of the southern hemisphere compared with
those of Europe, and especially with the observations made by an
Austrian astronomer Father Hell at Wardhus in Lapland, gave for the
distance of the sun the result which has since figured in all treatises
on astronomy and navigation.

No government hesitated in furnishing Academies with the means, however
expensive they might be, of conveniently establishing their observers in
the most distant regions. We hav