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 Titanum to the perturbations of the satellite’s path due to the surface features on Mars.  Observe that the principal 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 canals.  Whatever the origin of these features it is only necessary to assume 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 canals.  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 canals 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 canal?  The mass of the satellite; the state of the surface crust; the proximity of the satellite; and the amount of repetition 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 repetitions 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 mass might not become nodal to the satellite’s orbit, so that this passed 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 circumstances as reviewed above, among which crustal features have, in some cases, played a part.