Is it not astonishing to find in the commensurability of the mean motions of two planets, a cause of perturbation of so influential a nature; to discover that the definitive solution of an immense difficulty—­which baffled the genius of Euler, and which even led persons to doubt whether the theory of gravitation was capable of accounting 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 have already remarked that the determination of the contemplated distance appeared to demand imperiously an extensive base, for small bases would have been totally inadequate to the purpose.  Well, Laplace has solved the problem numerically without a base of any kind whatever; he has deduced the distance of the sun from observations of the moon made in one and the same place!