extreme cases. To look at this percentage in another light, the interest on the cost of a bridge for one year at four per cent will pay for the water-proofing.

In concrete bridges the relation between water-proofing costs and total costs is apparently a variable with wide limits, because the character of the pier-work exercises such a great influence on the latter figure. As a matter of fact, however, for certain types of bridges this relation is surprisingly uniform; but distinction must be made between two classes of concrete bridges, in order to arrive at the proper ratio. This is because of the cost of the protection or armor coat placed on the water-proofing. Such protection is always adopted for concrete railroad bridges of whatever type, and for earth-filled, solid-spandrel highway-bridges. These two then may be considered together. On flat-slab highway bridges, the protection coat is frequently omitted; and, if used, it is little more than a grouting course under the paving, which might be required even if the bridge were not water-proofed. This type of bridge constitutes the second class.

In the first class the cost of water-proofing bears about the same relation to the total cost as was found in the case of steel bridges—i.e., an average of four per cent. Isolated cases were encountered in railroad viaducts where the cost of water-proofing ran up to eight per cent; but this was exceptional, the usual cost being well under five per cent.

On flat-slab highway-bridges remarkable uniformity in relative costs was found. Ninety per cent of the cost figures which were analyzed showed the expense of water-proofing to be between one and a half and two per cent, and only a single bridge showed a greater cost. This last figure, therefore, may safely be taken as a fair average. Thus in all bridges, steel or concrete, except flat-slab-floor highway-bridges, the water-proofing cost is four per cent of the total, while in flat-slab-floor structures it is two per cent thereof.

The only element of cost which has not been considered is that of the interest on the investment; but this will not change the ratios which have already been arrived at, since the rate of increase in the cost of water-proofing through the addition of interest charges is, of course, identical with the rate of increase in the value of what the water-proofing is to protect, hence this element of cost may be ignored.

Probable Life of Water-Proofing

By the probable life of water-proofing is meant, of course, its effective life,—the length of time it will continue to exercise its water-excluding function. If a bridge has been properly designed with respect to water-proofing details, and if the water-proofing has been properly placed it will fail, if at all, from one or both of two causes,—a break in the continuity of the water-proofing envelope by rupture or otherwise, and the deterioration of the water-proofing  material  itself  by oxidation or rotting. The shock of