If the cartouche first falls and then rises, this shows the canal to have passed through a minimum state at the time denoted by the point of inflection; if it rises first and falls afterward, this betokens in the same way a maximum. Thus the cartouches reveal to us the complete history of the canals,—what changes they underwent and the times at which these occurred. The cartouche, then, is the graphic portrayal of the canal’s behavior. It not only distinguishes at once between the dead and the living, as we may call the effect of intrinsic change, but it tells the exact character of this change,—the way it varied from time to time, the epoch at which the development was at its minimum or its maximum for any given canal, and lastly, its actual strength at any time, thus giving its relative importance in the canal system. For the height of the curve above the diagrammatic horizon marks the absolute as well as the relative visibility and enables us to rank the canals between themselves. Now, the first point it furnishes a criterion for is the real or illusory character of the canals. If a line be due to illusion, whether optical or physical, it can vary only from extrinsic cause, since it has no intrinsic existence. If, therefore, all extrinsic cause be allowed for, the cartouche of this ghost must needs be a _horizontal straight line_. Even if the extrinsic factors to its production be imperfectly accounted for, their retention could only cause systematic variations from the straight line in all the lines, which would themselves vary systematically, and these factors could therefore be detected. This criterion is absolute. Unless all the cartouches were approximately straight lines, no illusion theory of any kind whatever could explain the facts. Even then the lines might all be real; for unchangeable reality would produce the same effect on the cartouches as illusion. In the case therefore of horizontal straight line cartouches, we should have no guarantee on that score of reality or illusion; but, on the other hand, curves or inclined straight lines in them would be instantly fatal to all illusion theories. Turning now to the 109 cartouches obtained in 1903, the first point to strike one’s notice is that all but three of them are curves and that even these three must be accepted with a caveat. Here, then, the cartouches dispose once and for all of any and every illusion theory. They show conclusively that the canals are real objects which wax and wane from some intrinsic cause.