But the history of our knowledge of the planet’s surface teaches us a different lesson. Two small objects appear repeatedly on the drawings made by Beer and Mädler in 1830; these are two similar dark spots, the one isolated, the other at the end of a gently curved line. Both spots resemble in form and character the oases of Prof. Lowell, and the curved line, at the termination of which one of the spots appears, represents closely the appearance presented by several of the canals. In the year 1830 no better drawings of Mars had appeared; and in representing these two spots as truly circular and the curved line as narrow, sharp, and uniform, Beer and Mädler undoubtedly portrayed the planet as actually they saw it. The one marking was named by Schiaparelli the Lacus Solis, the other, the Sinus Sabæus, and they are two of the best known and most easily recognized of the planet’s features; so that it is easy to trace the growth of our knowledge of both of them from 1830 up to the present time. They were drawn by Dawes in 1864, by Schiaparelli in 1877 and the succeeding years, by Lowell in 1894 and since, and by Antoniadi in 1909 and 1911. But whereas the drawings of Beer and Mädler, made by the aid of a telescope of 4 inches aperture, show the two spots as exactly alike, in those of Dawes, made with a telescope of 8 inches, the resemblance between the two has entirely vanished, and neither is shown as a plain circular dot. Since then, observers of greater experience and equipped with more powerful instruments have directed their attention to these two objects, and a mass of complicated structure has been brought out in the regions which were so simple in the sight of Beer and Mädler, so that not a trace of resemblance remains between the two objects that to them appeared indistinguishable.
Now the gradation in size, from the Lacus Solis down to the smallest oasis of Lowell, is a complete one. If a future development in the power of telescopes should equal the advance made from the 4-inch of Beer and Mädler, to the 33-inch which Antoniadi used in 1909, is it reasonable to suppose that Prof. Lowell’s oases will refuse to yield to such improvement, and will all still show themselves as uniform spots, precisely circular in outline? It is clear that Beer and Mädler would have been mistaken if they had argued that the apparently perfect circularity of the two oases which they observed proved them to be artificial, because the increase in telescopic power has since shown us that neither is circular. The obvious reason why they appeared so round to Beer and Mädler was that they were too small to be defined in their instruments; their minor irregularities were therefore invisible, and their apparent circularity covered detail of an altogether different form.
Beer and Mädler only drew two such spots; Lowell shows about two hundred. Beer and Mädler’s two spots seemed to them exactly alike; these two spots as we see them to-day have no resemblance to each other. Prof. Lowell’s two hundred oases, with few exceptions, seem all of the same character; is it possible to suppose, if telescopes develop in the future as they have done in the past, that the two hundred oases will preserve their uniformity of appearance any more than the Lacus Solis and the head of the Sinus Sabæus? If a novice begins to work upon Mars with a small telescope, he will draw the Lacus Solis and the Sinus Sabæus as two round, uniform spots, and as he gains experience, and his instrumental power is increased, he will begin to detect detail in them, and draw them as Dawes and Schiaparelli and others have shown them later. It is no question of planetary change; it is a question of experience and of “seeing.”
There is a much simpler explanation of the regularity of the canals and oases than to suppose that an industrious population of geometers have dug them out or planted them; it is connected with the nature of vision.
A telegraph wire seen against a background of a bright cloud can be discerned at an amazing distance—in fact, at 200,000 times the breadth of the wire; a distance at which the wire subtends a breadth of a second of arc. For average normal sight the perception of the wire will be quite unmistakable, but at the same time it would be quite untrue to say that the perception of the wire was of the nature of defined vision, as would be seen at once if small objects of irregular shape were threaded on the wire; these would have to be many times the breadth of the wire in order to be detected. Again, if instead of a wire of very great length extending right across the field of view of both eyes, a short, black line be drawn on a white ground, it will be found that as the length of the line is diminished below a certain point so its breadth must be increased. If the observer is distant from the line 6000 times its length, then the breadth must be increased to be equal to the length, and the object, whatever its actual shape, can be just recognized as a small circular spot, which will subtend about 34 seconds of arc.
But though a black spot, 34 seconds in diameter, can be perceived on a white ground, we have not yet attained to defined vision. For if we place two black spots each 34 seconds of arc in diameter, near each other, they will not be seen as separate spots unless there is a clear space between them of six times that amount. Nearer than that they will give the impression that they form one circular spot, or an oval one, or even a uniform straight line, according to the amount of separation. If two equal round spots be placed so that the distance between their centres is equal to two diameters, then the diameter of each spot must be, at least, 70 seconds of arc for them to be distinctly defined; that is to say for the spots to be seen as two separate objects.
It will be seen that there is a wide range between objects that are large enough to be quite unmistakably perceived, and objects which are large enough to have their true outline really defined. It is a question of seconds of arc in the one case and of minutes of arc in the other. Within this range, between the limit at which objects can be just perceived and that where they can be just defined, objects must all appear as of one of two forms—the straight line and the circular dot.
This depends upon the structure of the eye and of the retina; the eye being essentially a lens with its defining power necessarily limited by its aperture, and the retina a sensitive screen built up of an immense number of separate elements each of which can only transmit a single sensation. Different eyes will have different limits, both for the smallest objects which can be discerned and for the smallest objects that can be defined, but for any sight the range between the two will be of the order just indicated.
Prof. Lowell has drawn attention to the “strangely economic character of both the canals and oases in the matter of form.” It is true that straight lines and circles are economic forms, but they are economic not only in the construction of irrigation works but also in vision. “The circle is the figure which encloses the maximum area for the minimum average distance from its centre to any point situated within it;” therefore, if a small spot be perceived by the sight but be too small to have its actual outline defined, it will be recognized by the eye as being truly circular, on the principle of economy of effort. So, again, a straight line is the shortest that can be drawn between two points; and a straight line can be perceived as such when of an angular breadth quite 40 times less than that of the smallest spot. A straight line is that which gives the least total excitement in order to produce an appreciable impression, and therefore the smallest appreciable impression produces the effect of a straight line.
It is sufficient, then, for us to suppose that the surface of Mars is dotted over with minute irregular markings, with a tendency to aggregate in certain directions, such as would naturally arise in the process of the cooling of a planet when the outer crust was contracting above an unyielding nucleus. If these markings 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. They may be of any conceivable shape, provided 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 recognizes but cannot resolve) into lines essentially “canal-like” in character. Wherever there is a small aggregation of these minute markings, an impression will be given of a circular spot, or, to use Prof. Lowell’s nomenclature, an “oasis.” If the aggregation be greater still and more extended, we shall have a shaded area—a “sea.”