CONTENTS.

XVII

If the Abutment Wall be equally strong in every Part - 58

An Abutment Wall considered as an Arch - - 59

An Abutment Wall resisting an Uniform HorizontalForce, such as that of Wind - - - GO

An Abutment Wall, supporting a Fluid or Bank ofEarth - - - - - ib.

To determine the Extrados of an Arch and of its Piers 61To determine the Horizontal Thickness of a Bearing Pier 64

To determine the Curve , limiting the Extreme Points ofRange of Bodies projected, with a given HorizontalVelocity - - - - - 65

Formulas to determine the Numerical Quantities in theCases of the Circle , Ellipse , and Cycloid - - 66

Formulae to determine the Radius of Curvature to anyPoint in an Ellipse; Hyperbola , Parabola, Cycloid, Ca-tenary, and in the Catenary of Equal Strength at everyPoint - - - - - 70

TRACT III.

THE PRINCIPLES OF PENDENT BRIDGES, WITH REFERENCETO THE PROPERTIES OF THE CATENARY, APPLIED TOTHE MENAI BRIDGE.

Introduction ... Page 1

Natural Bridge by Suspension - -7

Table of Pendent Bridges - - - 10

Observations on the Strength and Stress of Chains formingCatenaries - - - - 12

Iron being the Material; the Maximum Ordinate to a givenAngle , and the Minimum Angle to a given Ordinate 17Table of the Strength of Materials - - 24

Table of the Weight of Materials, and of the Velocity andForce of Wind - - - - 26

To determine the Strength of the Cable Bridge proposedto be erected over the Strait of Menai, the Roadwaysuspended below the Cables

[a 2]

27