i's map (ante p. 166), we are given the course of the
lines as fragments of incomplete curves. Now these curves might
have been anything at all. We must take them as they are,
however, when we apply them as a test of the theory that the
motion of a satellite round Mars can strike such lines. If it can
be shown that satellites revolving round Mars might strike just
such curves then we assume this as an added confirmation of the
hypothesis.

We must begin by realising what sort of curves a satellite which
disturbs the surface of a planet would leave behind it after its
demise. You might think that the satellite revolving round and
round the planet must simply describe a circle upon the spherical
surface of the planet: a "great circle" as it is called; that is
the greatest circle which can be described upon a sphere. This
great circle can, however, only be struck, as you will see, when
the planet is not turning upon its axis: a condition not likely
to be realised.

This diagram (PI. XXI) shows the surface of a globe

188

covered with the usual imaginary lines of latitude and longitude.
The orbit of a supposed satellite is shown by a line crossing the
sphere at some assumed angle with the equator. Along this line
the satellite always moves at uniform velocity, passing across
and round the back of the sphere and again across. If the sphere
is not turning on its polar axis then this satellite, which we
will suppose armed with a pencil which draws a line upon the
sphere, will strike a great circle right round the sphere. But
the sphere is rotating. And it is to be expected that at
different times in a planet's history the rate of rotation varies
very much indeed. There is reason to believe that our own day was
once only 21/2 hours long, or thereabouts. After a preliminary rise
in velocity of axial rotation, due to shrinkage attending rapid
cooling, a planet as it advances in years rotates slower and
slower. This phenomenon is due to tidal influences of the sun or
of satellites. On the assumption that satellites fell into Mars
there would in his case be a further action tending to shorten
his day as time went on.

The effect of the rotation of the planet will be, of course, that
as the satellite advances with its pencil it finds the surface of
the sphere being displaced from under it. The line struck ceases
to be the great circle but wanders off in another curve--which is
in fact not a circle at all.

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