While Newton maintained that the form of the earth was that of a spheroid flattened at the poles, as a necessary sequence of the great natural law which bears his name, Jacques Cassini declared himself in favour of an elongated spheroid. The difference between these two illustrious teachers originated a controversy which lasted for upwards of fifty years. The Academy of Sciences of Paris pronounced, not unnaturally, in favour of the opinion of their colleague, though it was far from having the authority of Dominique Cassini, father of Jacques, and, still less, that of the illustrious President of the Royal Society of London. But patriotic ardour supplemented the weakness of their arguments. The flattened spheroid and Newton's law were rejected by France, because they were an English invention. Undoubtedly, no one _openly_ acknowledged so paltry a reason, but it was certainly true as a sentiment. As everybody knows, it was Voltaire who first removed the prohibition, and popularised the Newtonian philosophy in France. How did our astronomers finally succeed in demonstrating mathematically the veritable form of our planet? To obtain a clear and accurate conception, we are obliged to transport ourselves back two thousand years. Let us recall, in the first place, that, owing to the diurnal movement, all the stars progress from east to west; that they rise and set, to recommence the same rotation. This is a general and conspicuous fact, which everybody can confirm for himself. But now for another, whose observation requires a little more time and patience. During the diurnal movement, which carries on all the stars and the sun himself, the latter progresses independently, in the inverse direction of the celestial vault, as a fly might do upon a revolving globe. But this second fact is complicated with a third: While advancing on his own account, from west to east, the circle which the sun traverses is not parallel to the Equator; the radiant luminary transports himself alternatively into the northern and southern hemispheres, accomplishing this rotation in 365 days and a fraction of a day, in an oblique plane, which cuts that of the Equator under an angle of about 23-1/2°. * * * * * Let us here take advantage of a parenthesis to explain a few astronomical technicalities, necessary for the due comprehension of our subject.