g much larger than those on the other. I would show the picture
here, but it is too large. One of these days, it will be given in a
book I am going to write about Mars, who is quite important enough to
have a book all to himself. I want you, now, to understand me that
Mars really does travel in a most complicated path, when you consider
the earth as at rest. If a perfect picture of all his loopings and
twistings since astronomy began could be drawn,--even on a sheet of
paper as large as the floor of a room,--the curves would so interlace
that you would not be able to track them out, but be always leaving
the true track and getting upon one crossing it slightly aslant,--just
like the lines by which trains are made to run easily off one
track on to another.

The unfortunate astronomers of old times, who had to explain, _if they
could_, this complicated behavior of Mars (and of other planets, too),
were quite beaten. The more carefully they made their observations,
the more peculiar the motions seemed. One astronomer gave up the work
in despair, just like that unfortunate Greek philosopher who, because
he could not understand the tides of the Euboean Sea, drowned
himself in it. So this astronomer, who was a king,--Alphonsus of
Portugal,--unable to unravel the loops of the planets, said, in his
wrath, that if he had been called on by the Creator to assign the
planets their paths, he would have managed the matter a great deal
better. The plates of the old astronomical books became more and more
confusing, and cost more and more labor, as astronomers continued to

... "Build, unbuild, contrive
To save appearances, to gird the sphere
With centric and eccentric scribbled o'er,
Cycle and epicycle, orb in orb."

It was to the study of Mars, the wildest wanderer of all, that we owe
the removal of all these perplexities. The idea had occurred to the
great astronomer, Copernicus, that the complexities of the planets'
paths are not real, but are caused by the constant moving about of the
place from whence we watch the planets. If a fly at rest at the middle
of a clock face watched the ends of the two hands, they would seem to
go round him in circles; but if, instead, he was on the end of one of
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 awa