pounced upon this idea and ultimately evolved the following
scheme. "The earth is the sphere, the measure of all; round it describe
a dodecahedron; the sphere including this will be Mars. Round Mars
describe a tetrahedron; the sphere including this will be Jupiter.
Describe a cube round Jupiter; the sphere including this will be Saturn.
Now, inscribe in the earth an icosahedron, the sphere inscribed in it
will be Venus: inscribe an octahedron in Venus: the circle inscribed in
it will be Mercury." With this result Kepler was inordinately pleased,
and regretted not a moment of the time spent in obtaining it, though to
us this "Mysterium Cosmographicum" can only appear useless, even without
the more recent additions to the known planets. He admitted that a
certain thickness must be assigned to the intervening spheres to cover
the greatest and least distances of the several planets from the sun,
but even then some of the numbers obtained are not a very close fit for
the corresponding planetary orbits. Kepler's own suggested explanation
of the discordances was that they must be due to erroneous measures of
the planetary distances, and this, in those days of crude and infrequent
observations, could not easily be disproved. He next thought of a
variety of reasons why the five regular solids should occur in precisely
the order given and in no other, diverging from this into a subtle and
not very intelligible process of reasoning to account for the division
of the zodiac into 360 deg.. The next subject was more important, and dealt
with the relation between the distances of the planets and their times
of revolution round the sun. It was obvious that the period was not
simply proportional to the distance, as the outer planets were all too
slow for this, and he concluded "either that the moving intelligences of
the planets are weakest in those that are farthest from the sun, or that
there is one moving intelligence in the sun, the common centre, forcing
them all round, but those most violently which are nearest, and that it
languishes in some sort and grows weaker at the most distant, because of
the remoteness and the attenuation of the virtue". This is not so near a
guess at the theory of gravitation as might be supposed, for Kepler
imagined that a repulsive force was necessary to account for the planets
being sometimes further from the sun, and so laid aside the idea of a
constant attractive force. He made several other attempts to