of others, while the values of some factors may remain unchanged. The costs of these various factors tend to balance, so that considerable modifications rarely produce great changes in total cost. This principle is true for all kinds of factors. For instance, in determining the economic span lengths for a truss bridge, increasing the span-length augments the cost per lineal foot for the superstructure and generally, but not always, reduces that of the substructure. Again, in contrasting carbon steel and alloy steel for bridgework, the latter gives smaller weights but greater costs per pound. Also, in comparing railway decks of the ordinary wooden type with ballasted floors, the first cost of the latter is greater, but the expense for its maintenance is less; and this last condition is generally found when pitting steel bridges against reinforced concrete ones.

The effects of variations in factors can be well comprehended by a study of the various diagrams for Chapter XVIII, which treats of the economic span-lengths for simple-truss bridges on various types of foundations at different depths below the elevation of Low Water. The plotted curves show costs per lineal foot for superstructure, substructure, and the total. It will be noted that all substructure curves are concave upward, that the superstructure records are either right lines or easy curves also concave upward, and that the lines for totals are generally very flat curves, concave upward. The economic span-length occurs where the steepness of the substructure curve is just the same as that of the superstructure curve, but it will be noted from the upper of the three curves (the one for total costs per lineal foot) that varying twenty-five feet either way from the absolute minimum augments very slightly, indeed, the total cost per foot, and that a variation therefrom of fifty feet seldom increases the said cost more than two per cent. Furthermore, the exact minimum is dependent somewhat upon the personal equation of the designer; for such matters as sizes of pier bases must be determined largely by judgment, and a slight variation in unit prices of materials in place will move the lowest point of curve some distance horizontally.

From the foregoing it is evidently a waste of time to split hairs when one knows he is near the economic point; but, on the other hand, adopting a span-length of 450 feet when 300 feet is the economic limit may sometimes add ten or fifteen per cent to the total cost of structure, consequently one must make sure that his adopted span-lengths do not differ too seriously from those for truly greatest economy.

There is another economic fact that is well worth noting, viz., that whenever in reducing the span-length, some important part reaches minimum size, so that further diminution in length will not reduce that part, it is practically certain that a shorter length will not be economic.

In nearly all economic studies for bridges, the lighter the superimposed load the greater will be the economic length, whether it be span, panel, stringer-spacing, or what-not. This is largely due to the fact that, in case of any design, as the distance in question is reduced, if the loading were