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did not arise from any telescopic observations that he made, or, indeed, that any one else
made. They were all elaborately deduced from Tycho's measurements of the positions of the
planets, obtained with his great instruments, which were unprovided with telescopic
assistance.
To realise the tremendous advance which science received from Kepler's great work, it is to be
understood that all the astronomers who laboured before him at the difficult subject of the
celestial motions, took it for granted that the planets must revolve in circles. If it did not
appear that a planet moved in a fixed circle, then the ready answer was provided by Ptolemy's
theory that the circle in which the planet did move was itself in motion, so that its centre
described another circle.
When Kepler had before him that wonderful series of observations of the planet, Mars, which
had been accumulated by the extraordinary skill of Tycho, he proved, after much labour, that
the movements of the planet refused to be represented in a circular form. Nor would it do to
suppose that Mars revolved in one circle, the centre of which revolved in another circle. On no
such supposition could the movements of the planets be made to tally with those which Tycho
had actually observed. This led to the astonishing discovery of the true form of a planet's
orbit. For the first time in the history of astronomy the principle was laid down that the
movement of a planet could not be represented by a circle, nor even by combinations of
circles, but that it could be represented by an elliptic path. In this path the sun is situated at
one of those two points in the ellipse which are known as its foci.
Very simple apparatus is needed for the drawing of one those ellipses which Kepler has shown
to possess such astonishing astronomical significance. Two pins are stuck through a sheet of
paper on a board, the point of a pencil is inserted in a loop of string which passes over the
pins, and as the pencil is moved round in such a way as to keep the string stretched, that
beautiful curve known as the ellipse is delineated, while the positions of the pins indicate the
two foci of the curve. If the length of the loop of string is unchanged then the nearer the pins
are together, the greater will be the resemblance between the ellipse and the circle, whereas
the more the pins are separated the more elongated does the ellipse become. The orbit of a
great planet is, in general, one of those ellipses which approaches a nearly circular form. It
fortunately happens, however, that the orbit of Mars makes a wider departure from the
circular form than any of the other important planets. It is, doubtless, to this circumstance
that we must attribute the astonishing success of Kepler in detecting the true shape of a
planetary orbit. Tycho's observations would not have been sufficiently accurate to have
exhibited the elliptic nature of a planetary orbit which, like that of Venus, differed very little
from a circle.
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The more we ponder on this memorable achievement the more striking will it appear. It must
be remembered that in these days we know of the physical necessity which requires that a
planet shall revolve in an ellipse and not in any other curve. But Kepler had no such
knowledge. Even to the last hour of his life he remained in ignorance of the existence of any
natural cause which ordained that planets should follow those particular curves which
geometers know so well. Kepler's assignment of the ellipse as the true form of the planetary
orbit is to be regarded as a brilliant guess, the truth of which Tycho's observations enabled
him to verify. Kepler also succeeded in pointing out the law according to which the velocity of
a planet at different points of its path could be accurately specified. Here, again, we have to
admire the sagacity with which this marvellously acute astronomer guessed the deep truth of
nature. In this case also he was quite unprovided with any reason for expecting from physical
principles that such a law as he discovered must be obeyed. It is quite true that Kepler had
some slight knowledge of the existence of what we now know as gravitation. He had even
enunciated the remarkable doctrine that the ebb and flow of the tide must be attributed to the
attraction of the moon on the waters of the earth. He does not, however, appear to have had
any anticipation of those wonderful discoveries which Newton was destined to make a little
later, in which he demonstrated that the laws detected by Kepler's marvellous acumen were
necessary consequences of the principle of universal gravitation.
To appreciate the relations of Kepler and Tycho it is necessary to note the very different way
in which these illustrious astronomers viewed the system of the heavens. It should be
observed that Copernicus had already expounded the true system, which located the sun at
the centre of the planetary system. But in the days of Tycho Brahe this doctrine had not as yet
commanded universal assent. In fact, the great observer himself did not accept the new views
of Copernicus. It appeared to Tycho that the earth not only appeared to be the centre of
things celestial, but that it actually was the centre. It is, indeed, not a little remarkable that a
student of the heavens so accurate as Tycho should have deliberately rejected the Copernican
doctrine in favour of the system which now seems so preposterous. Throughout his great
career, Tycho steadily observed the places of the sun, the moon, and the planets, and as
steadily maintained that all those bodies revolved around the earth fixed in the centre. Kepler,
however, had the advantage of belonging to the new school. He utilised the observations of
Tycho in developing the great Copernican theory whose teaching Tycho stoutly resisted.
Perhaps a chapter in modern science may illustrate the intellectual relation of these great
men. The revolution produced by Copernicus in the doctrine of the heavens has often been
likened to the revolution which the Darwinian theory produced in the views held by biologists
as to life on this earth. The Darwinian theory did not at first command universal assent even
among those naturalists whose lives had been devoted with the greatest success to the study
of organisms. Take, for instance, that great naturalist, Professor Owen, by whose labours vast
extension has been given to our knowledge of the fossil animals which dwelt on the earth in
past ages. Now, though Owens researches were intimately connected with the great labours
of Darwin, and afforded the latter material for his epoch-making generalization, yet Owen
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deliberately refused to accept the new doctrines. Like Tycho, he kept on rigidly accumulating
his facts under the influence of a set of ideas as to the origin of living forms which are now
universally admitted to be erroneous. If, therefore, we liken Darwin to Copernicus, and Owen
to Tycho, we may liken the biologists of the present day to Kepler, who interpreted the results
of accurate observation upon sound theoretical principles.
In reading the works of Kepler in the light of our modern knowledge we are often struck by
the extent to which his perception of the sublimest truths in nature was associated with the
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