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.
The more we ponder on this memorable achievement the more striking
will it appear.
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