it was necessary to modify some of the items for the increased diameter of tube and the steeper approach grades, also to omit the costs of equipment and administration, as these are not included in the bridge estimates. For the modification of cost due to a changed diameter of tube, it was assumed that the cost per lineal foot increases and decreases as the square of the exterior diameter. This assumption is almost exactly correct, because the thickness of the shell varies directly with the diameter, as does also the length of the periphery, consequently, the volume of the shell is approximately proportional to the square of the diameter. Again, the volume of excavation for any shield driven, circular tunnel varies as the square of the diameter; and as almost the entire cost per lineal foot is that of the shell plus that of the excavation, it is evident that the assumption mentioned is justified.

Increasing the exterior diameter of the tube to thirty-one (31) feet makes the interior diameter twenty-seven (27) feet. This is just enough to provide a clear roadway of twenty-two (22) feet in the highway tunnel and allows just enough space for two lines of the widest subway cars in the electric-railway tunnel.

In the latter type it is feasible to contrast the cost of a double-track tube with that of two single-track tubes; but in a highway tunnel it is not, because a breakdown of a single vehicle would block all traffic until it is hauled out by sending a double-ender wrecking-car into the tube in a reverse direction to that of the traffic. With such an occurrence in a double-track tunnel, the automobiles could pass by the wrecked vehicle.

If there were an accidental stoppage of an electric railway car in a single-track tube, it would cause no more obstruction to rail traffic than it would if the accident had taken place in a double-track tube that operates in both directions.

The author computed all the quantities of materials in substructure, superstructure, and approaches of six structures, in order to plot the two cost curves for bridges shown in Fig. 6a. On that diagram are given the total costs for bridges with their approaches and for tunnels with their approaches based upon the unit prices which governed at the time the tunnel estimates were prepared. The principal ones of these are as follows:

In proportioning the substructures the author made the dimensions as small as considerations of true efficiency would permit, and did not attempt any beautification of structure by an unnecessary enlargement of piers. If these are properly built to meet all possible conditions of loading and so as to provide against future deterioration caused by the elements, that ought to suffice; and so doing should be deemed good engineering practice.