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:— Cartouche. Character. 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.