cantilever bridges. — Typical layouts for cantilever bridges. — Comparison of weights of metal in cantilevers and three simple spans of same total length. — Conditions favoring Type C cantilevers. — Conditions favoring Type A cantilevers. — Cantilever and simple-truss layouts for equal cost. — New economic consideration in cantilevering and dissertation there-on ................ 83

Reasons for making this economic investigation. — Economics for ends free and ends

anchored. — Dr. Steinman's book on this subject and its incorrectness. — Labor involved in this investigation was excessive and why. — Assumptions for the investigation. — Unit prices of materials in place. — Costs of tracks omitted and why. — Using short cuts in computations. — Diagrams recording results. — Modification of an established formula. — Division of nickel steel and carbon steel. — Equity of comparisons. — Method of figuring quantity of concrete for anchorages. — Load on piles. — Limiting widths of structures. — Economic lengths for cantilever structures. — Splay. — Investigation for double-track-railway bridges and its results. — Effect of supporting anchorages on piles. — Investigation for combined-railway-and-highway bridges and its results. — Variations in data between Dr. Steinman's and the author's investigations. — Uneconomics involved by assuming too long anchor arms. — Errors in Dr. Steinman's substructure costs. — Error in his tower weights. — Re-computation of Dr. Steinman's case by author and results thereof. — Tabulated comparison of Dr. Steinman's and author's substructure costs. — Tribute to Dr. Steinman's energy and ability. — Consolation for his wrong conclusion. — Investigation for highway bridges and results thereof. — Résumé of investigations. — Effect of using high-alloy steel. — Addendum. — Proposed suspension bridge of 2500-ft. span for Detroit. — Unit prices used for metal in place. — Effect on economics due to abnormal unit prices in 1919. — Practical proof of usefulness of this investigation ................................. 90

Conditions affecting the economics. — Maintenance, repairs, and depreciation

must be considered. — Also cost of renewals, danger from fire, etc. — Interruption of traffic in making repairs. — Embankments. — Timber trestles. — Right-of-way. — Abutments versus buried piers. — Steel trestle versus reinforced-concrete trestle. — Spiral approaches. — Timber trestles.  — Embankments ..........113

Importance of this economic problem. — Fallacy of general idea of economic struc-

ture being one involving least first-cost. — List of items to consider. — Gov-