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in gravitating and stretching into the funi-cular curve, assumes a thickness, as will beshewn hereafter, in proportion to the secantof the angle made at the point of the curvebetween a horizontal line and the tangentat that point; that is, thinnest at the apex,gradually increasing in thickness to thepoints of suspension, accommodating itsstrength economically to the tensions at theseveral points of the curve. The bridgebeing now constructed, the spider begins todescend; and, by observing her progress,it will be seen that the angle (made by thetangent at the point of the curve, with ahorizontal line, where the insect is) be-comes increased by her weight, and the ten-sion, in respect to the catenarian form,there consequently reduced; and alsothroughout the curve on that side the apex;and, therefore, the ordinate of the curve isalways shorter than the corresponding or-dinate on the other side, where there isno incumbent weight, and where the ten-sion, in respect of the catenarian form, isincreased.

Thus the bridge adjusts itselfj first by