ASTRONOMY 
311 
These latter movements take place in a plane which cuts 
at an angle the equator of the heavenly sphere; the several 
orbits are parts of what Plato calls the ‘ circle of the Other 
as distinguished from the ‘ circle of the Same which is the 
daily revolution of the heavenly sphere as a whole and which, 
carrying the circle of the Other and the seven movements 
therein along with it, has the mastery over them. The result 
of the combination of the two movements in the case of any 
one planet is to twist its actual path in space into a spiral 1 ; 
the spiral is of course included between two planes parallel to 
that of the equator at a distance equal to the maximum 
deviation of the planet in its course from the equator on 
either side. The speeds with which the sun, the moon and 
the five * planets describe their own orbits (independently 
of the daily rotation) are in the following order; the moon is 
the quickest; the sun is the next quickest and Venus and 
Mercury travel in company with it, each of the three taking 
about a year to describe its orbit; the next in speed is Mars, 
the next Jupiter, and the last and slowest is Saturn; the 
speeds are of course angular speeds, not linear. The order 
of distances from the earth is, beginning with the nearest, 
as follows : moon, sun, Venus, Mercury, Mars, Jupiter, Saturn. 
In the Republic all these heavenly bodies describe their own 
orbits in a sense opposite to that of the daily rotation, i. e. in 
the direction from west to east; this is what we should 
expect; but in the Timaeus we are distinctly told, in one 
place, that the seven circles move ‘ in opposite senses to one 
another ’, 2 and, in another place, that Venus and Mercury 
have ‘ the contrary tendency ’ to the sun. 3 This peculiar 
phrase has not been satisfactorily interpreted. The two state 
ments taken together in their literal sense appear to imply 
that Plato actually regarded Venus and Mercury as describing 
their orbits the contrary way to the sun, incredible as this 
may appear (for on this hypothesis the angles of divergence 
between the two planets and the sun would be capable of any 
value up to 180°, whereas observation shows that they are 
never far from the sun). Proclus and others refer to attempts 
to explain the passages by means of the theory of epicycles; 
Chalcidius in particular indicates that the sun’s motion on its 
1 Tinmens, 38 e-39 b. 2 Ik 36 n. 3 Ik 38 n.