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|the “canals„ of mars||261|
impression either 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, 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 very wide range between objects which are large enough to be quite unmistakeably 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 minutes of arc in the other.
This depends upon the structure of the eye and 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 object that can be discerned, and for the smallest object that can be defined, but for any sight the range between the two will be of the order just indicated. Between these two limits, — the limit of discernment and the limit of definition, — objects can only appear under the two forms of straight lines and of round spots. Mr Lowell is justified in drawing attention to «the strangely economic character of both the canals and oases in the matter of form». («Mars», page 187). Straight lines and circles are economic forms, but they are economic not only in hypothetical hydraulic undertakings, but also in vision. «The circle is the figure which incloses the maximum area for the minimum average distance from its centre to any point situated within it»; («Mars», page 187); therefore if a small spot be perceived by the sight, but be too small to have its actual outline defined, it will be recognised by the eye as 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.