4. Diplopia might be a respecter of persons, but it certainly could not be one of canals. For a given observer it must be objectively general in its application to the same class of objects. Consequently, if the doubling were diplopic, all canals inclined at the same angle to the vertical—for the tilt might affect the result were the eye astigmatic—should be similarly affected. Parallel canals should parallel each other’s action. With the Martian doubles this is not the case. Of two canals similarly inclined the one will be double, the other not, at the same instant and under conditions that are alike. And this persistently. For gemination is an attribute of certain canals and never of others. At a given season of the Martian year, some canals are regularly double, some invariably single. Night after night and presentation after presentation these idiosyncrasies are preserved: the doubles, always pairs, the single, always alone. Nor does the strength of the line affect the action. The single canals are some of them stronger, some of them weaker, than the doubles seen at the same time. 5. If of diplopic origin the mean width of all the doubles should be the same. For though the diplopic width would vary for a given canal according to the moment, a sufficient number of views would yield a mean width which would be the same for all. Tilt apart, the mean width of one canal would be that of another. Among Martian doubles, on the contrary, I have found the width to be a specific property of the particular canal. Each has its own mean width regardless of inclination, and this individual width differs as between one and another by as much as five to two, or, if we consider such canals as the Nilokeras I and II, by more than ten to two. Any one of these five points is fatal to the theory; _a fortiori_ all. _II. The Interference Theory_ From the wave propagation of light it follows that the image of a bright line made by a lens is not itself a simple bright line but a bright band flanked by alternate dark and bright ones. It has, therefore, been suggested that a bright medial line is here concerned and that the double canal is the first of its dark pair of outriders. But the suggestion does not bear scrutiny. 1. It presupposes a central streak brighter than the rest of the disk to give birth to the twin dark lines. This should itself be visible in the image; but no such bright backbone is seen. 2. It demands a perfectly definite width of separation for a given aperture—which is not that observed. 3. It makes the width a function of the aperture, decreasing as this increases—which is not sustained by observation. Different apertures produce no effect on the widths of the Martian doubles, as the writer has shown (Lowell Observatory Bulletin, No. 5) by a change of aperture from twenty-four to six inches.