169

TO FIND THE CURVE WHICH A PERFECTLY FLEXIBLESTRING WILL FORM BY THE POWER OF GRAVITY, WHENSUSPENDED FROM TWO POINTS, THE THICKNESS OF IT,THAT IS, THE AREA OF ITS SECTION, BEING AT EVERYPOINT AS THE TENSION AT THAT POINT.

Suppose ACB to represent the curverequired, CG a string of the same densityand thickness as ACB at the vertex C, andof such a length as to produce by its weightat the higher point the same tension asthat at the vertex of the curve; and FHanother string of the same density andthickness as CG, and of such a length asby its weight to produce the same tensionat the higher point, as that in the curve atthe point F.

A

D

B