Part 30

This effect is at its maximum along two particular parallel lines which are tangents to the circle of maximum horizontal stress and which run parallel with the path of the satellite. The distance separating these lines depend upon the elevation of the satellite above the planet's surface. Such lines mark out the theoretical axes of the "double canals" which future crustal movements will more fully develop.

It is interesting to consider what the effect of such

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conditions would be if they arose at the surface of our own planet. We assume a horizontal force in the crust adequate to set up tensile stresses of the order, say, of fifteen tons to the square foot and these stresses to be repeated every few hours; our world being also subject to the dynamic effects we recognise in and beneath its crust.

It is easy to see that the areas over which the satellite exerted its gravitational stresses must become the foci --foci of linear form--of tectonic developments or crust movements. The relief of stresses, from whatever cause arising, in and beneath the crust must surely take place in these regions of disturbance and along these linear areas. Here must become concentrated the folding movements, which are under existing conditions brought into the geosynclines, along with their attendant volcanic phenomena. In the case of Mars such a concentration of tectonic events would not, owing to the absence of extensive subaerial denudation and great oceans, be complicated by the existence of such synclinal accumulations as have controlled terrestrial surface development. With the passage of time the linear features would probably develop; the energetic substratum continually asserting its influence along such lines of weakness. It is in the highest degree probable that radioactivity plays no less a part in Martian history than in terrestrial. The fact of radioactive heating allows us to assume the thin surface crust and continued sub-crustal energy throughout the entire period of the planet's history.

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How far willl these effects resemble the double canals of Mars? In this figure and in the calculations I have given you I have supposed the satellite engaged in marking the planet's surface with two lines separated by about the interval separating the wider double canals of Mars--that is about 220 miles apart. What the distance between the lines will be, as already stated, will depend upon the height of the satellite above the surface when it comes upon a part of the crust in a condition to be affected by the stresses it sets up in it. If the satellite does its work at a point lower down above the surface the canal produced will be narrower. The stresses, too, will then be much greater. I must also observe that once the crust has yielded to the pulling stress, there is great probability that in future revolutions of the satellite a central fracture will result. For then all the pulling force adds itself to the lifting force and tends to crush the crust inwards on the central line beneath the satellite. It is thus quite possible that the passage of a satellite may give rise to triple lines. There is reason to believe that the canals on Mars are in some cases triple.

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.

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.

You will readily see how we find this curve. Suppose the sphere to be rotating at such a speed that while the satellite is advancing the distance Oa, the point b on the

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sphere will be carried into the path of the satellite. The pencil will mark this point. Similarly we find that all the points along this full curved line are points which will just find themselves under the satellite as it passes with its pencil. This curve is then the track marked out by the revolving satellite. You see it dotted round the back of the sphere to where it cuts the equator at a certain point. The course of the curve and the point where it cuts the equator, before proceeding on its way, entirely depend upon the rate at which we suppose the sphere to be rotating and the satellite to be describing the orbit. We may call the distance measured round the planet's equator separating the starting point of the curve from the point at which it again meets the equator, the "span" of the curve. The span then depends entirely upon the rate of rotation of the planet on its axis and of the satellite in its orbit round the planet.

But the nature of events might have been somewhat different. The satellite is, in the figure, supposed to be rotating round the sphere in the same direction as that in which the sphere is turning. It might have been that Mars had picked up a satellite travelling in the opposite direction to that in which he was turning. With the velocity of planet on its axis and of satellite in its orbit the same as before, a different curve would have been described. The span of the curve due to a retrograde satellite will be greater than that due to a direct satellite. The retrograde satellite will have a span more than half

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way round the planet, the direct satellite will describe a curve which will be less than half way round the planet: that is a span due to a retrograde satellite will be more than 180 degrees, while the span due to a direct satellite will be less than 180 degrees upon the planet's equator.

I would draw your attention to the fact that what the span will be does not depend upon how much the orbit of the satellite is inclined to the equator. This only decides how far the curve marked out by the satellite will recede from the equator.

We find then, so far, that it is easy to distinguish between the direct and the retrograde curves. The span of one is less, of the other greater, than 180 degrees. The number of degrees which either sort of curve subtends upon the equator entirely depends upon the velocity of the satellite and the axial velocity of the planet.

But of these two velocities that of the satellite may be taken as sensibly invariable, when close enough to use his pencil. This depends upon the law of centrifugal force, which teaches us that the mass of the planet alone decides the velocity of a satellite in its orbit at any fixed distance from the planet's centre. The other velocity--that of the planet upon its axis--was, as we have seen, not in the past what it is now. If then Mars, at various times in his past history, picked up satellites, these satellites will describe curves round him having different spans which will depend upon the velocity of axial rotation of Mars at the time and upon this only.

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In what way now can we apply this knowledge of the curves described by a satellite as a test of the lunar origin of the lines on Mars?