To see this the more clearly, we may set over against the cartouche the canal character it signalizes:—
A horizontal straight line. Canal invariable. A straight line tilted up on the right. Canal increasing steadily. A straight line tilted up on the left. Canal decreasing steadily. A curved line descending, concave from Canal decreasing, but more above. and more slowly. A curved line ascending, concave from Canal increasing, but more above. and more rapidly. A curved line descending, convex from Canal decreasing more and above. more rapidly. A curved line ascending, convex from Canal increasing more and above. more slowly. A curved line first descending, then Canal decreasing more and ascending, concave from above more slowly to a minimum, throughout. thence increasing more and more rapidly. A curved line first descending, then Canal increasing more and ascending, convex from above more slowly to a maximum, throughout. thence decreasing more and more rapidly.
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.