Kepler must also be remembered as one of the first great astronomers who ever had the privilege of viewing celestial bodies through a telescope.  It was in 1610 that he first held in his hands one of those little instruments which had been so recently applied to the heavens by Galileo.  It should, however, be borne in mind that the epoch-making achievements of Kepler 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.

[Plate:  Kepler.]

Very simple apparatus is needed for the drawing of one of 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