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It follows therefore that, if the actual surface of Mars were really covered by a network of straight lines, like those represented on the charts which we owe to Mr Lowell, there could be no doubt, no controversy about their existence. Every observer would see them, since an actual straight line can be seen when its angular breadth is very far indeed below the limit of vision for any other form.
It is sufficient then for us to suppose that the surface of Mars is dotted over with minute irregular markings. If these are fairly near each other, it is not necessary in order to produce the effect of «canals», that they should be individually large enough to be seen, nor is it necessary that these markings should approximately be circular in actual form. They may be of any conceivable shape, provided only that they are separately below the limit of defined vision, and are sufficiently sparsely scattered. In this case the eye inevitably sums up the details which it recognises, (but cannot resolve) into lines, essentially canal-like in character. Wherever there is a slight aggregation of these minute markings, we shall have the impression of a circular spot, or to use Mr Lowell’s nomenclature, an «oasis». If the aggregation be greater still, and more extended, we shall have a shaded area, — a «sea».
The above considerations arise from simple experiments with the unaided eye, but the same principle apply yet more strongly to telescopic vision. I would refer the reader to a series of valuable papers on this subject by Dr G. Johnstone Stoney in the «Philosophical Magazine» Vol. XVI, pp. 318, 796, and 950 (1908, Aug., Nov., and Dec.). It need simply be noted here, — since the images of a mathematical point, and of a mathematical line are not represented by a telescope as a mathematical point and line respectively, but as small surfaces, — that minute irregularities are inevitably smoothed out by the telescope. A magnifying power of 250 applied to a telescope directed on the Moon will not show the lunar structure so well, as we should see it without a telescope, if it were brought within a thousand miles of us. Mars, at its nearest approach, is more than 150 times the distance of the Moon, yet certainly no observer, using a magnifying power of 150 has ever seen Mars as well as we can see the full Moon with naked eye. I am of course allowing for the fact that Mars has double the diameter of the Moon. Telescopic vision, more-