Having demonstrated the smallness of these periodic oscillations, Laplace next succeeded in determining the absolute dimensions of the orbits. What is the distance of the sun from the earth? No scientific question has occupied the attention of mankind in a greater degree. Mathematically speaking, nothing is more simple: it suffices, as in ordinary surveying, to draw visual lines from the two extremities of a known base line to an inaccessible object; the remainder of the process is an elementary calculation. Unfortunately, in the case of the sun, the distance is very great and the base lines which can be measured upon the earth are comparatively very small. In such a case, the slightest errors in the direction of visual lines exercise an enormous influence upon the results. In the beginning of the last century, Halley had remarked that certain interpositions of Venus between the earth and the sun--or to use the common term, the transits of the planet across the sun's disk--would furnish at each observing station an indirect means of fixing the position of the visual ray much superior in accuracy to the most perfect direct measures. Such was the object of the many scientific expeditions undertaken in 1761 and 1769, years in which the transits of Venus occurred. A comparison of observations made in the Southern Hemisphere with those of Europe gave for the distance of the sun the result which has since figured in all treatises on astronomy and navigation. No government hesitated to furnish scientific academies with the means, however expensive, of establishing their observers in the most distant regions. We have already remarked that this determination seemed imperiously to demand an extensive base, for small bases would have been totally inadequate. Well, Laplace has solved the problem 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.