Routledge History of Philosophy Volume IV

108 SCIENCE AND MATHEMATICS UP TO DESCARTES
was traditional in at first seeking for a circular orbit and reintroducing an equant
point, although not necessarily at the same distance as the Sun from the centre of
the orbit. In this manner he formed a developed theory, which he later called his
‘vicarious hypothesis’; it became especially famous for a crucial deviation of
eight minutes of arc from observational evidence, which would previously have
been undetectable.
Since the divine goodness has given to us in Tycho Brahe a most careful
observer, from whose observations the error of 8 minutes in the Ptolemaic
account (calculus) is argued in Mars, it is fitting that with grateful mind we
should recognise and cultivate this gift of God…. For if I had treated these
8 minutes of longitude as negligible, I should already have sufficiently
corrected the hypothesis…. But because they could not be neglected, these
eight minutes alone have led the way to reforming the whole of astronomy,
and have been made the matter for a great part of this work. 23
With the vicarious hypothesis rejected, Kepler embarked on a bewildering
variety of sophisticated procedures. One strategy was to place the Earth more on
a par with the other planets; for it provided the moving platform from which we
observed, but hitherto its orbit had lacked an equant point. To this end Kepler
found it useful to imagine that he was on Mars and observing the Earth from
there. Another strategy was that of quantifying the causes of the
planetary motions. A force emanating from the Sun, and inversely proportional
to the distance from the Sun, was conceived as pushing the planets around. This
eventually led to what we know as Kepler’s second law of planetary motion, that
the radius vector from the Sun to a planet sweeps out equal areas in equal times.
But this force did not explain a planet’s varying distance from the Sun. For this
purpose a quasi-magnetic push-pull force was introduced with allusion to
William Gilbert’s De magnete which had been published in 1600. This caused a
libration of the planet on an epicycle’s diameter directed towards the Sun. With
this theoretical apparatus Kepler proceeded to seek the actual path of Mars. For
this he experimented with a variety of egg-shaped orbits. Readers of Gulliver’s
Travels will remember that eggs have big ends and little ends, but Kepler did use
ellipses as calculating devices, and eventually came with a start to a realization
that the orbit itself was an ellipse, with the Sun at one focus (the ‘first law’).
O, how ridiculous of me! As if the libration in the diameter could not be a
way to the ellipse. I have become thoroughly convinced that the ellipse
stands together with the libration, as will be evident in the next chapter,
where at the same time it will be demonstrated that no figure remains for
the orbit of the planet other than a perfectly elliptical one. 24
Kepler’s first two laws (which were soon generalized to the other planets) were
published, with a detailed account of his procedures, in 1609 in his Astronomia