In the latter paper the curves of weights of metal for cantilever bridges were extended far beyond the limits of accurate computations by a method specially evolved for the purpose; and, while the said method may not be deemed strictly accurate, it is truly logical and, in all probability, close enough for the economic investigations in the making of which its resulting weights were employed. From the weights plotted in the "speculative zone" of Fig. 7 in that paper, and herein reproduced as Fig. 5c, has been prepared Fig. 5d, from which can be found the comparative economics of any procurable or practically-possible high-alloy steels for cantilever structures having main spans exceeding the longest yet constructed, viz., the 1,800 ft. span of the Quebec Bridge.

The following example will illustrate its use:

Example No. 5

What are the comparative economics of standard nickel steel costing in place 8.5 cents per pound and an alloy steel having an elastic limit of 80,000 lbs. per square inch and costing in place 11.2 cents per pound, for a three-span, cantilever bridge which has a main opening of 2,450 feet?

From Fig. 5d we find the comparing ratios of weights, in relation to a hypothetical steel having an elastic limit of 100,000 lbs. per square inch, to be 1.23 and 1.66; hence, compared with each other, the ratio of average weights per foot for the two materials will be 1.23 ÷ 1.66 = 0.74. The ratio of pound prices erected is 11.2 ÷ 8.5 = 1.318. The product of these ratios is 1.318 X 0.74 = 0.98. As this is less than unity, the high-alloy steel is more economic than the standard nickel steel, and the saving involved is about two per cent.

It may be noticed that in this last investigation there is an implied assumption to the effect that the steel for the structures is unmixed, or, in other words, that carbon steel is not employed for light members or minor parts. The explanation for this is four-fold.

First. In such long spans it pays to cut out every possible pound of dead load.

Second. Everything connected with the structure being on a stupendous scale, there will be no members so light as to be proportioned for rigidity and not for strength.

Third. In the detailing of heavy members of alloy steel, it will generally be advisable to use the alloy so as to make the details themselves as strong as possible.

Fourth. Even if there were a small amount of carbon steel employed in these phenomenally long and heavy bridges, the percentage thereof in any two compared cases of alloy steels of different elastic limits would be so nearly alike that the reliability of Fig. 5d would not be affected.

A question has been raised as to the accuracy of the curves in Figs. 5a and 5b, on the plea that the relative amounts of nickel steel and carbon