I have spoken all along of the satellite moving slowly over the surface of Mars.  I have done so as I cannot at all pronounce so readily on what will happen when the satellite’s velocity over the surface of Mars is very great.  To account for all the lines mapped by Lowell some of them must have been produced by satellities moving relatively to the surface of Mars at velocities so great

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as three miles a second or even rather more.  The stresses set up are, in such cases, very difficult to estimate.  It has not yet been done.  Parallel lines of greatest stress or impulse ought to be formed as in the other case.

I now ask your attention to another kind of evidence that the lines are due in some way to the motion of satellites passing over the surface of Mars.

I may put the fresh evidence to which I refer, in this way:  In Lowell’s map (P1.  XXII, p. 192), and in a less degree in Schiaparelli’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

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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.