To sum up: the figurative grouping of the stars, the variety of their luminous magnificence, their position towards Polaris, the determination of that position by the longitudinal circles passing through the axis of the world, and twisted perpendicularly to this axis by the circles parallel to the Equator,--such is the aggregate of the elements which must, at a very early period, have presided over the enumeration of those sparkling points, each of which is the centre of a system. * * * * * Finally, are there any stars which the eye cannot perceive? Such a question would never have been propounded to the ancients. And why? Because no reasoning would have drawn from them an admission that it was possible by artificial means to enlarge the range of our eyesight. They would have deemed it madness to pretend to improve and develope what is not of human creation; the visual apparatus, as it is bestowed on us by nature, they supposed to be the most perfect instrument which man could imagine. And, in truth, nothing could fairly be objected to this way of looking at things. * * * * * The 48 constellations (21 northern, 12 zodiacal, and 15 austral) indicated by Ptolemæus, contain a total of 1026 stars, whose relative positions had been determined by Hipparchus. To undertake an enumeration of the stars, and to transmit the result to posterity, appeared to Pliny an audacity before which even a god would have recoiled (_Hipparchus--ausus, rem etiam Deo improbam, annumerare posteris stellas_).[11] Yet numerous doubts had already risen in the mind of Hipparchus as to the accuracy of the number recognised. In the first place, the ancients undoubtedly knew, as we do, that the visual faculty is not the same in all individuals; that there are some who, in the same celestial space, see more stars than others. Many persons can discern up to stars of the seventh magnitude, while with others the sight fails far within that limit. The ancients must also have known, as we do, that, for the enumeration to be complete, the sky must be observed from all the points of the terrestrial surface on which man is planted. Even in our own days the catalogues of the southern heavens are far from being perfect. Finally, more than two thousand years before the time of Galileo, Democritus had already enunciated the opinion that the Milky Way was a mass of innumerable stars. All these signs should have been accepted as warnings against premature affirmations. * * * * *