CONTENTS.

XIX

To determine the Number of Square Indies in the CollectiveSections of Chains supporting a Road , 10 Cases Page 84To determine the Catenary, when the Number of SquareInches, the Weight of the Chains , the Force to over-come the Cohesion of them, the Weight of the Road,and any one of the Five Catenarian Quantities, except

the Tension, are given, 5 Cases - - 87

To determine the greatest Catenary which can be formed,the Materia], and any one of the Catenarian Quantities, ,except the Tension, being given - - 88

Use of the Table of the Dimensions of the Catenary,

15 Cases and Examples - - 90

Theoretical Investigation of the Catenary - 101

Definitions - - - - -101

Theorem. — The Points of Suspension may be changedwithout altering the Tension in any other Point of theCatenary - - - - 102

Problem. — To investigate the Equations of the Catenary 104Problem.—Any Two of the Catenarian Quantities beinggiven, to find the other Four, 15 Cases - 109

Geometrical Method of expressing the Tension at anyPoint of a Catenary - - - - 115

Theorem. — Catenaries making Equal Angies with theirOrdinates, are similar - - - 116

Problem. — To find the Angle when the Tension is aMinimum in respect to the Ordinate - - 118

Problem. — To find the Sub tangent to a Catenary - 121

Corollary. — The Tension, when a Minimum in respectto the Ordinate equals the Subtangent - - ib.

Problem.—Given any One of Five Catenarian Quantities,to find the other Four Geometrically, when the Tensionis a Minimum in respect to the Ordinate, 5 Cases - 122

Problem. — To find Geometrically any Three of theFive Catenarian Quantities, the other Two being given,

20 Cases ... _ _ jge

[a 3]