fountains, the ebb and flow of the tides, the shape of the continents
and inland seas, and things of this sort". Following his tutor in his
admiration for the Copernican theory, he wrote an essay on the primary
motion, attributing it to the rotation of the earth, and this not for
the mathematical reasons brought forward by Copernicus, but, as he
himself says, on physical or metaphysical grounds. In 1595, having more
leisure from lectures, he turned his speculative mind to the number,
size, and motion of the planetary orbits. He first tried simple
numerical relations, but none of them appeared to be twice, thrice, or
four times as great as another, although he felt convinced that there
was some relation between the motions and the distances, seeing that
when a gap appeared in one series, there was a corresponding gap in the
other. These gaps he attempted to fill by hypothetical planets between
Mars and Jupiter, and between Mercury and Venus, but this method also
failed to provide the regular proportion which he sought, besides being
open to the objection that on the same principle there might be many
more equally invisible planets at either end of the series. He was
nevertheless unwilling to adopt the opinion of Rheticus that the number
six was sacred, maintaining that the "sacredness" of the number was of
much more recent date than the creation of the worlds, and could not
therefore account for it. He next tried an ingenious idea, comparing the
perpendiculars from different points of a quadrant of a circle on a
tangent at its extremity. The greatest of these, the tangent, not being
cut by the quadrant, he called the line of the sun, and associated with
infinite force. The shortest, being the point at the other end of the
quadrant, thus corresponded to the fixed stars or zero force;
intermediate ones were to be found proportional to the "forces" of the
six planets. After a great amount of unfinished trial calculations,
which took nearly a whole summer, he convinced himself that success did
not lie that way. In July, 1595, while lecturing on the great planetary