But let us take the figures given in the text for the intervals between the Earth and the seven “planets” arranged in the same order, and again taking the Earth to Moon distance as unity, we have:-- TABLE II (_of intervals_) Interval between ♁ and ☽ = 5,554,130 stadia or _x_ “ ” ☽ “ ☉ = 11,088,260 ” 2_x_ “ ” ☉ “ ♀ = 16,632,390 ” 3_x_ “ ” ♀ “ ☿ = 22,176,520 ” 4_x_(2²) “ ” ☿ “ ♂ = 49,897,170 ” 9_x_(3²) “ ” ♂ “ ♃ = 44,353,040 ” 8_x_(2³) “ ” ♃ “ ♄ = 149,691,510 ” 27_x_(3³) This agrees almost entirely with the theory which M. Bigourdan in the work mentioned in the last note has worked out as the Platonic theory of the distances of the different planets from the Earth, “the supposed centre of their movements” (p. 228). Thus:-- Planets ☽ ☉ ♀ ☿ ♂ ♃ ♄ Distances 1 2 3 4 8 9 27 which distances are, in his own words, “les termes enchevêtrés de deux progressions géométriques ayant respectivement pour raison 2 et 3, savoir 1, 2, 4, 8--1, 3, 9, 27; on voit que l’unité est, comme chez Pythagore, la distance de la Terre à la Lune.” This conclusion is amply borne out by Hippolytus’ figures, which, as given in Table II above, show a regular progression from 2 and 3 to 2² and 3², then to 2³ and 3³, which explains what our author means by increasing the Earth to the Moon distance, κατὰ τὰ διπλάσιον καὶ τριπλάσιον. The only discrepancy between this and M. Bigourdan’s table is that he has transposed the distances between ☿--♂ and ♂--♄ respectively; but as I do not know the details of the calculation on which he bases his figures, I am unable to say whether the mistake is his or Hippolytus’.] [Footnote 67: Are we to conclude from this that these last calculations are those of Claudius Ptolemy, the author of the _Almagest_? He has certainly not been mentioned before, but his fame was so great that Hippolytus may have been certain that the allusion would be understood by his audience. Ptolemy lived, perhaps, into the last quarter of the second century.] [Footnote 68: Genesis vi. 4. The subject seems to have had irresistible fascination for Christian converts of Asiatic blood, whether orthodox or heretic. Manes also wrote a book upon the Giants, cf. Kessler, _Mani_, Berlin, 1899, pp. 191 ff.] [Footnote 69: Hippolytus seems to have been entirely ignorant that the calculations he derides were anything but mere guesswork. They were not only singularly accurate considering the imperfection of the observations at the disposal of their author, but have also been of the greatest use to science as laying the foundation of all future astronomy.] [Footnote 70: ἀμέτρους. Another pun on their _measurements_.]