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.

The sun is, with respect to our satellite the moon, the cause of perturbations which evidently depend on the distance of the immense luminous globe from the earth.  Who does not see that these perturbations must diminish if the distance increases, and increase if the distance diminishes, so that the distance determines the amount of the perturbations?  Observation assigns the numerical value of these perturbations; theory, on the other hand, unfolds the general mathematical relation which connects them with the solar distance and with other known elements.  The determination of the mean radius of the terrestrial orbit—­of the distance of the sun—­then becomes one of the most simple operations of algebra.  Such is the happy combination by the aid of which Laplace has solved the great, the celebrated problem of parallax.  It is thus that the illustrious geometer found for the mean distance of the sun from the earth, expressed in radii of the terrestrial orbit, a value differing but slightly from that which was the fruit of so many troublesome and expensive voyages.

The movements of the moon proved a fertile mine of research to our great geometer.  His penetrating intellect discovered in them unknown treasures.  With an ability and a perseverance equally worthy of admiration, he separated these treasures from the coverings which had hitherto concealed them from vulgar eyes.  For example, the earth governs the movements of the moon.  The earth is flattened; in other words, its figure is spheroidal.  A spheroidal body does not attract as does a sphere.  There should then