In this manner were obtained the cartouches of 109 canals. Now, as the presence or absence of any canal in any drawing was entirely irrespective of the presence or absence of another, each such datum spoke only for itself, and was an entirely independent observation. The whole investigation thus rested on 10,900 completely separate determinations, each as unconditioned by the others as if it existed alone.
As every factor outside of the canal itself which could affect the latter’s visibility was taken account of, and the correction due to it as nearly as possible applied before the cartouches were deduced, the latter represent the visibility of the canal due to intrinsic change alone. In other words, they give not the apparent only but the real history of the canal for the period concerned.
Important disclosures result from inspection of the cartouches. This we shall perceive by considering what different curves mean in the case. If the canal were an unchangeable phenomenon, for any reason whatever, its cartouche would be a straight line parallel to the horizon of the diagram. This is evident from the fact that the visibility would then never vary. If, on the other hand, it were waxing and waning, and the wax or wane were uniform, the cartouche would be a straight line inclined to the horizontal; rising if the canal were increasing, falling when it decreased. Lastly, if the rate of change itself varied, the cartouche would be a curve concave or convex to the line denoting the time, according as the rate of change of the growth or decay grew greater or less.
To see this the more clearly, we may set over against the cartouche the canal character it signalizes:—
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.
The second result afforded by the cartouches is not of a destructive, negative character,—however valuable the destruction of bars to knowledge may be,—but of a constructive, positive one. It does not, like the first, follow from mere inspection, but is brought to light only by comparison of all the cartouches. In a positive way, therefore, its testimony is as conclusive as it was in a negative direction. For that 10,900 separate and independent data should result in a general law of development through either conscious or unconscious bias, when those data would have to be combined in so complicated a manner for the result to emerge as is here the case, is impossible. Chance could not do it and consciousness would require a coördinate memory, to which Murphy’s nine games of chess at once would be child’s play.