if the cost had been the real value R, would be a'R + L'. As before, these two values are equal; and, therefore,

Equating the two values of V gives

and

"Now, if the value thus found for R be greater than the cost C', the second bridge is more economical than the first; while, if it be less, the first bridge will be the more economical."

It will be noted that the foregoing method does not mention costs of operation and maintenance. They can be taken into account by adding their capitalized costs to the costs C and C'.

Conditions sometimes arise which render it inadvisable to adopt the most economic of the several compared types of construction—for instance, when the promoters cannot possibly raise the money required to build the kind of structure which they desire, and, consequently, must content themselves, for a time at least, with one that is inferior. An example of this is a proposed railroad through virgin country, where the cheapest kind of a line will serve to develop business, and will suffice for many years to take care of the traffic, although uneconomically as compared with first-class railroads. Under such conditions an engineer possessed of sound financial judgment would advocate building the line at first as cheaply as practicable; adopting comparatively heavy grades, sharp curves, cheap ties, light rails, temporary structures, earth ballast, low-power locomotives, etc.; but paying strict attention to the vital matter of thorough drainage, and studying in advance of construction the question of how the line can be improved later at least expense and without materially interfering with traffic.

As another illustration of this economic consideration, there might be taken the case of a bridge for a crossing where there is danger from washout of falsework. Here it would be advisable to adopt a cantilever structure instead of a layout of simple-truss spans, notwithstanding the fact that it might require considerably more metal and might involve a higher pound price for erection.

Such problems as these may be deemed by some people to be questions of expediency rather than of economics; but the author prefers to treat them as pertaining to the latter, which means that, in the case first mentioned, he would consider it truly economic to build the cheap line and operate it for a while uneconomically rather than to spend at the outset large sums of money in order, later on, to handle economically traffic that possibly might fail ever to materialize; and that in the second case it would