XX

CONTENTS.

Theorem Iutrod active to the Construction of the Cate-nary ... _ p a g e 129

Corollary. — To draw a Logarithmic Curve to a givenSubtangent - - - - 152

Problem. — From the Tension at the Vertex to constructan Indefinite Catenary - - - 132

Problem. — Two of the Six Quantities being given, toconstruct the Catenary, 6 Cases - 134

Problem. — To find the Area of the Space bounded bythe Catenary, and its Absciss, and Ordinate - 139

Problem. — To find the Radius of Curvature of the Ca -tenai’y - - - - - - 140

Problem. — To find the Centre of Gravity of the Cate-nary - - - - - - 141

Explanation of the Table of Dimensions of a Catenary 143Table of Formulas for the Catenary - - - 145

Table of the Dimensions of a Catenary which may be usedfor a Table of Sines, Tangents , Secants, and Cosecants 147To find the Curve of the Catenary, whose Thickness isat every Point as the Tension at that point - - 169

To construct this Catenary - - - -174

Table of Formulae for this Catenary - - - 177