This is the last of the three heavens in which Dante has met spirits whose lives did not reach the perfection of the saints in higher heavens, but were marred by broken vows, earthly ambition, earthly love; and here he is reminded that he has not yet soared high enough to be beyond reach of the cone of shadow thrown by the earth. This is another allegory resting on what was to the poet an astronomical fact. For Earth’s shadow was said by Ptolemy and Alfraganus to extend to 268 times the distance of her semi-diameter, and the distance of Venus from Earth varied, according to Alfraganus, between 167 and 1120 times this unit, while the next planet, the sun, at his least distance was 1120 units distant (the same as Venus’ greatest). Therefore the spheres of Venus and the two nearer planets Mercury and the Moon, were all within reach of Earth’s shadow, but the sun and the rest were far beyond it.[664] Venus and Mercury themselves never could be actually touched by the shadow like the moon, however, because they keep too near the sun for Earth to interpose herself between them and the source of light. (Though the length of the shadow thrown by Earth is nearly accurate, see pp. 191-92, the planets are a great deal further than Alfraganus supposed; for the least distance of Venus is nearly 6000 times Earth’s semi-diameter, and the least distance of Mercury 12,000). ------------------------------------------------------------------------ [664] Rabbi Abraham ben Chija, in his _Sphæra Mundi_, written about 1100 A.D., says that Earth’s shadow extends as far as the distance of Mercury, not of Venus (Delambre, _Histoire de l’astronomie ancienne_, and Dreyer, _Planetary Systems_); but this does not agree with the figures given by Alfraganus. ------------------------------------------------------------------------ Except for this we have only the passage in the _Paradiso_ already referred to, where Dante, standing among the stars of Gemini, found the sphere above him too distant to be seen, but turning his gaze downwards was able to survey all the planets and the earth at the centre of the World. He knew very well that at a distance from Earth 20,000 times her own semi-diameter it would be impossible to see her as a disc,[665] far less to distinguish oceans and continents, hills and river-mouths. It would in fact be like looking at an object one foot in diameter at a distance of two miles. But as we have before observed, his power of vision here was more than human: at every step in this marvellous journey it had grown clearer and stronger, and in the fourth heaven he had been able to look on spirits which shone in the sun more brilliantly than the sun itself, although on earth no eye can look upon the sun.[666] In the Empyrean, distinctions of space, and impediments to vision vanished altogether.[667]