AS EXHIBITED IN THE TENTH BOOK OF "THE REPUBLIC." 311 



S, 4, and 5, and thus being the psychogenic cube, as Anatolius calls it ( Theolog. Anthon. p. 40, 

 ed. Ast.), because it is the period of the Pythagorean metempsychosis. On the other hand, 

 there are 7 terms in the double tetractys, and the sum of the first six is represented by the 

 seventh : for 1 + 2 + 3 + 4 + 8 + 9 «= 27. Lastly, if we take the mean proportionals between 

 8 and 27, namely, 12 and 18, we get the musical ratio ^. And as the other musical ratio ^ 

 represents the sides including the right angle in the sacred triangle, and these added together 

 make the sacred number 7, so the other sacred number 5 may be resolved into the constituent 

 parts 2 and 3, and the numbers 7 and 5 when added together make another regulative number 

 of mysterious import, the number of months in the 

 year. In his moral and political speculations Plato was 

 met by the same numbers. There were 4 cardinal 1 



virtues, 3 parts of the human soul, and 5 forms of 



•3 2 



government; and I have shown elsewhere that, in the 



Republic (p. 546), the mystical period of the state is _ . 



defined by an elaborate calculation, which amounts to 



4"' , 2' , „ , , . . , 27 18 12 , 8 



the equation — . 5 = — . 10^ all these bemg musical 

 3* o 



and Pythagorean numbers, and being cubed according 



to the theory of harmonic completeness, just as in p. 587 c, the number 729, i. e. 9', represents 

 the misery of the tyrant, because he is nine times as wretched as the oligarch. The number 

 7 reappears in the Laws (v. p. 737), where Plato limits his citizens to 5040, dpiOfiov tji/o? 

 evexa irpoariKovTo^, i. e. because this is the continued product of the first seven digits. 



Applying these considerations to the passage before us, we see at once the reason for the 

 seven days spent in the meadow, and the Jive days occupied on the journey to the center of 

 light. The eight hoops of the wheel are of course the regions belonging to the seven planets 

 and the fixed stars. And the order of the planets is that which is given in the Timceus 

 (p. 38), where, as here, the positions of Venus and Mercury are interchanged. For the order 

 of the eight concentric hoops, beginning with the outermost, is as follows: 1st the fixed 

 stars, 2nd Saturn, 3rd Jupiter, 4th Mars, 5th Mercury, 6th Venus, 7th the Sun, 8th the 

 Moon; the Earth being the axis of the system. The colours of the planets themselves are 

 supposed to be communicated by their motion to the orbits which they traverse. The differ- 

 ent widths of the hoops indicate the different inclinations of the orbits to the plane of the 

 ecliptic. But the intervals intended are regulated by the successive terms of the double 

 tetractys {Timceus, p. S6 b); thus: 



The introduction of the Sirens, as diminutive figures small enough to stand on the sepa- 

 rate hoops of the wheel, is sanctioned by the plastic art of the Greeks in Plato's time. 

 The great statue of Juno in the Heraeum at Argos, which was set up by Polycleitus towards 

 the end of the Peloponnesian war, had a crown adorned with sculptured figures of the Horsa 

 Vol. X. Part II. 40 



