the hands (and was not knocked off as the other passed), the end of
this other hand would not move round the fly in the same simple way.
When the two hands were together it would be near, when they were
opposite it would be far away, and, without entering into any
particular description of the way in which it would seem to move, you
can easily see that the motion would seem much more complicated
than if the fly watched it from the middle of the clock face. Now,
Copernicus _did_ enter into particulars, and showed by mathematical
reasoning that nearly all the peculiarities of the planets' motions
could be explained by supposing that the sun, not the earth, was the
body round which the planets move, and that they go round him nearly
in circles.

[Illustration: FIG. 3. THE PATHS OF MARS, THE EARTH, VENUS, AND
MERCURY.]

But Copernicus could not explain _all_ the motions. And Tycho Brahe,
another great astronomer, who did not believe at all in the new ideas
of Copernicus, made a number of observations on our near neighbor
Mars, to show that Copernicus was wrong. He gave these to Kepler,
another great astronomer, enjoining him to explain them in such a way
as to overthrow the Copernican ideas. But Kepler behaved like Balaam
the son of Beor; for, called on to curse (or at least to denounce) the
views of Copernicus, he altogether blessed them three times. First,
he found from the motions of Mars that the planets do not travel in
circles, but in ovals, very nearly circular in shape, but not having
the sun exactly at the center. Secondly, he discovered the law
according to which they move, now faster now slower, in their oval
paths; and thirdly, he found a law according to which the nearer
planets travel more quickly and the farther planets more slowly,