between students of technical schools. — Tests made by the author of the "B. E." methods of making quick cost-computations in bridgework. — Eleven examples solved in the making of quick estimates. — Quick estimates for suspension bridges. — Statement of the student problems ................. 141

But little known previously concerning true economic span-lengths for varying

substructure conditions. — Author's mathematical solution of three decades ago and its limitations. — Special investigation made by actual estimates of cost of over two hundred piers with their spans. — Instigation of the investigation was the series of studies for the proposed New Orleans bridge. — Assumptions and conditions for investigation. — Character of structures. — Methods of pier sinking. — Specifications for designing. — Loads. — Permissible pressures on soil and piles. — Unit prices of materials in place. — Method of determining the economic span-length. — Recording-diagrams and table. — Resume of results of computations. — Deductions. — Check on old method of determining economic span-lengths. — Relative weights of metal in equal-truss, three-span bridges and structures of the same kind, same total length, and same loading, but having the central span lengthened and the other two equally shortened......... 150

Old method of designing masonry piers. — Author's experience in designing piers

for Red Rock Cantilever bridge. — Day of cut-stone-masonry piers is past. — Copings. — Economics of reinforcing for traction effects. — Dumb-bell piers. — Hollow shafts to reduce load on foundations. — Piers composed of two cylinders. — Mattresses. — Temporary piers. — Cocked hat. — Cutting down and rebuilding of main piers of the Fratt Bridge at Kansas City. — Ice-breakers. — Reinforced-concrete versus timber for cribs and caissons of bridge piers. — Steel versus timber for concrete forms. — Best depth to carry pier-shaft below low-water mark. — Reduction of pier size to avoid lessening the area of water-way. — Clearance in crib around base of shaft. — Pneumatic process versus open-dredging. — Coffer-dam method versus open-dredging. — Comparative economics of open-dredging caisson and pile-filled crib. — Economics of employing both the pneumatic and the open-dredging processes on the piers for same bridge. — Economics of hastening pier sinking. — Comparative economics of stepping off plain-concrete bases or spreading suddenly by using reinforcing bars. — Reinforced concrete piles versus wooden ones ..................... 167

This problem cannot be solved by complicated mathematics, but only by making

actual competitive designs and estimates of cost. — Mathematical solution of economic truss-depths.  —   Economic depths of  plate-girder spans and