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Let the angle DBC, which the cate- Fig. 9.nary makes with a horizontal line be7°„10', and BI (r 116 feet,) the height ofthe pier at B. Draw B A at right anglesto the tangent of the catenary at B, inter-secting the base of the pier in A. Makethe width of the pier = 2 AI; then, as rad.

: tang. ^7° 10" :: 116 : 14.5, hence 2 A I= 29 feet, which is about the fourth of itsheight; which, with reference to practice,seems a proper proportion in this case.

Let the length of the ordinate D Bof the catenary be 250 feet, then thelength of the curve will be 250.655 feet;so that if the pier were B A W, and vi-brated upon the point A, V A could notassume the place of A W, so long as thehorizontal resistance remained constant.

The parabolic curve, B V W, will be ob-tained by the example before given, B Wbeing the same in this as I K in that; B Wbeing the greatest range of a projectedbody on a horizontal plane, B W, insteadof the greatest range on the inclined planeB K.*

* The catenarian B W may be obtained easily from the