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

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covered with the usual imaginary lines of lat.i.tude and longitude.

The orbit of a supposed satellite is shown by a line crossing the sphere at some a.s.sumed angle with the equator. Along this line the satellite always moves at uniform velocity, pa.s.sing 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 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 a.s.sumption 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 pa.s.ses 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...o...b..t 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...o...b..t 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 ma.s.s of the planet alone decides the velocity of a satellite in its...o...b..t 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?

To do this we must apply to Lowell's map. We pick out preferably, of course, the most complete and definite curves. The chain of ca.n.a.ls of which Acheron and Erebus are members mark out a fairly definite curve. We produce it by eye, preserving the curvature as far as possible, till it cuts the equator. Reading the span on the equator we find' it to be 255 degrees. In the first place we say then that this curve is due to a retrograde satellite. We also note on Lowell's map that the greatest rise of the curve is to a point about 32 degrees north of the equator. This gives the inclination of the satellite's...o...b..t to the plane of Mars'

equator.

With these data we calculate the velocity which the planet must have possessed at the time the ca.n.a.l was formed on the hypothesis that the curve was indeed the work of a satellite. The final question now remains If we determine the curve due to this velocity of Mars on its axis, will this curve fit that one which appears on Lowell's map, and of which we have really availed ourselves of only three points? To answer this question we plot upon a sphere, the curve of a satellite, in the manner I have described, a.s.signing to this sphere the velocity derived from the span of 255 degrees. Having plotted the curve on the sphere it only remains to transfer it to Lowell's map. This is easily done.

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This map (Pl. XXII) shows you the result of treating this, as well as other curves, in the manner just described. You see that whether the fragmentary curves are steep and receding far from the equator; or whether they are flat and lying close along the equator; whether they span less or more than 180 degrees; the curves determined on the supposition that they are the work of satellites revolving round Mars agree with the mapped curves; following them with wonderful accuracy; possessing their properties, and, indeed, in some cases, actually coinciding with them.

I may add that the inadmissible span of 180 degrees and spans very near this value, which are not well admissible, are so far as I can find, absent. The curves are not great circles.

You will require of me that I should explain the centres of radiation so conspicuous here and there on Lowell's map. The meeting of more than two lines at the oases is a phenomenon possibly of the same nature and also requiring explanation.

In the first place the curves to which I have but briefly referred actually give rise in most cases to nodal, or crossing points; sometimes on the equator, sometimes off the equator; through which the path of the satellite returns again and again.

These nodal points will not, however, afford a general explanation of the many-branched radiants.

It is probable that we should refer such an appearance

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as is shown at the Sinus t.i.tanum to the perturbations of the satellite's path due to the surface features on Mars. Observe that the princ.i.p.al radiants are situated upon the boundary of the dark regions or at the oases. Higher surface levels may be involved in both cases. Some marked difference in topography must characterise both these features. The latter may possibly originate in the destruction of satellites. Or again, they may arise in crustal disturbance of a volcanic nature, primarily induced or localised by the crossing of two ca.n.a.ls. Whatever the origin of these features it is only necessary to a.s.sume that they represent elevated features of some magnitude to explain the multiplication of crossing lines. We must here recall what observers say of the multiplicity of the ca.n.a.ls. According to Lowell, "What their number maybe lies quite beyond the possibility of count at present; for the better our own air, the more of them are visible."

Such innumerable ca.n.a.ls are just what the present theory requires. An in-falling satellite will, in the course of the last 60 or 80 years of its career, circulate some 100,000 times over Mars' surface. Now what will determine the more conspicuous development of a particular ca.n.a.l? The ma.s.s of the satellite; the state of the surface crust; the proximity of the satellite; and the amount of repet.i.tion over the same ground. The after effects may be taken as proportional to the primary disturbance.

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It is probable that elevated surface features will influence two of these conditions: the number of repet.i.tions and the proximity to the surface. A tract 100 miles in diameter and elevated 5,000 or 10,000 feet would seriously perturb the orbit of such a body as Phobos. It is to be expected that not only would it be effective in swaying the orbit of the satellite in the horizontal direction but also would draw it down closer to the surface. It is even to be considered if such a ma.s.s might not become nodal to the satellite's...o...b..t, so that this pa.s.sed through or above this point at various inclinations with its primary direction. If acting to bring down the orbit then this will quicken the speed and cause the satellite further on its path to attain a somewhat higher elevation above the surface. The lines most conspicuous in the telescope are, in short, those which have been favoured by a combination of circ.u.mstances as reviewed above, among which crustal features have, in some cases, played a part.

I must briefly refer to what is one of the most interesting features of the Martian lines: the manner in which they appear to come and go like visions.

Something going on in Mars determines the phenomenon. On a particular night a certain line looks single. A few nights later signs of doubling are perceived, and later still, when the seeing is particularly good, not one but two lines are seen. Thus, as an example, we may take the case of Phison and Euphrates. Faint glimpses of the dual state were detected in the summer

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and autumn, but not till November did they appear as distinctly double. Observe that by this time the Antarctic snows had melted, and there was in addition, sufficient time for the moisture so liberated to become diffused in the planet's atmosphere.

This increase in the definition and conspicuousness of certain details on Mars' surface is further brought into connection with the liberation of the polar snows and the diffusion of this water through the atmosphere, by the fact that the definition appeared progressively better from the south pole upwards as the snow disappeared. Lowell thinks this points to vegetation springing up under the influence of moisture; he considers, however, as we have seen, that the ca.n.a.ls convey the moisture. He has to a.s.sume the construction of triple ca.n.a.ls to explain the doubling of the lines.

If we once admit the ca.n.a.ls to be elevated ranges--not necessarily of great height--the difficulty of accounting for increased definition with increase of moisture vanishes. We need not necessarily even suppose vegetation concerned. With respect to this last possibility we may remark that the colour observations, upon which the idea of vegetation is based, are likely to be uncertain owing to possible fatigue effects where a dark object is seen against a reddish background.

However this may be we have to consider what the effects of moisture increasing in the atmosphere of Mars will be with regard to the visibility of elevated ranges,

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We a.s.sume a serene and rare atmosphere: the nights intensely cold, the days hot with the unveiled solar radiation. On the hill tops the cold of night will be still more intense and so, also, will the solar radiation by day. The result of this state of things will be that the moisture will be precipitated mainly on the mountains during the cold of night--in the form of frost--and during the day this covering of frost will melt; and, just as we see a heavy dew-fall darken the ground in summer, so the melting ice will set off the elevated land against the arid plains below.

Our valleys are more moist than our mountains only because our moisture is so abundant that it drains off the mountains into the valleys. If moisture was scarce it would distil from the plains to the colder elevations of the hills. On this view the accentuation of a ca.n.a.l is the result of meteorological effects such as would arise in the Martian climate; effects which must be influenced by conditions of mountain elevation, atmospheric currents, etc. We, thus, follow Lowell in ascribing the accentuation of the ca.n.a.ls to the circulation of water in Mars; but we a.s.sume a simple and natural mode of conveyance and do not postulate artificial structures of all but impossible magnitude.

That vegetation may take part in the darkening of the elevated tracts is not improbable. Indeed we would expect that in the Martian climate these tracts would be the only fertile parts of the surface.

Clouds also there certainly are. More recent observations

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appear to have set this beyond doubt. Their presence obviously brings in other possible explanations of the coming and going of elevated surface features.

Finally, we may ask what about the reliability of the maps? About this it is to be said that the most recent map--that by Lowell--has been confirmed by numerous drawings by different observers, and that it is,itself the result of over 900 drawings. It has become a standard chart of Mars, and while it would be rash to contend for absence of errors it appears certain that the trend of the princ.i.p.al ca.n.a.ls may be relied on, as, also, the general features of the planet's surface.

The question of the possibility of illusion has frequently been raised. What I have said above to a great extent answers such objections. The close agreement between the drawings of different observers ought really to set the matter at rest. Recently, however, photography has left no further room for scepticism.

First photographed in 1905, the planet has since been photographed many thousands of times from various observatories.

A majority of the ca.n.a.ls have been so mapped. The doubling of the ca.n.a.ls is stated to have been also so recorded.[1]

The hypothesis which I have ventured to put before you involves no organic intervention to account for the

[1] E. C. Slipher's paper in _Popular Astronomy_ for March, 1914, gives a good account of the recent work.

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details on Mars' surface. They are physical surface features.

Mars presents his history written upon his face in the scars of former encounters--like the shield of Sir Launcelot. Some of the most interesting inferences of mathematical and physical astronomy find a confirmation in his history. The slowing down in the rate of axial rotation of the primary; the final inevitable destruction of the satellite; the existence in the past of a far larger number of asteroids than we at present are acquainted with; all these great facts are involved in the theory now advanced. If justifiably, then is Mars' face a veritable Principia.