It may be argued that such calculations are utterly useless, because the data on which the computations are based are variable and to some extent non-computable, and therefore no dependence can be placed on the calculations. This is true to the extent that it is useless to claim any great precision in the computation of the value of any proposed change of alinement. In the numerical ease suggested above it is assumed that the saving amounts to only \$720 per year. The cost of making the change is very easily computed. If it is found that it can be done at a total expenditure of say \$3000, then there is hardly any question of the advisability of making the change, for, with all the allowance which can reasonably be made in the method of computing the effect of the change, we can be sure that the final result is not in error by several times the true result. The question is not so much as to whether our computed capitalized value, \$14,400, is mathematically precise or even correct to within 10%. The method of computation gives a value which is fairly close and which will give a rational measure of the advisability of making the change. If the cost of the improvement very nearly equals the computed capitalized value, then it will probably make but little difference whether the improvement is made or not. Such a question would then depend more on the difficulty of raising money for the improvement. Also, if it is shown that the cost of making the improvement is far greater than the capitalized value of the improvement as computed, then there is hardly any doubt that the improvement is not justifiable.

To express the above question more generally, in every computation of the operating value of a proposed improvement, it may always be shown that the true value lies somewhere between some maximum and some minimum. Closer calculations and more reliable data will narrow the range between these extreme values. According as the interest on the cost of the proposed improvement is greater or less than the mean of these limits, we may judge of its advisability. The range of the limits shows the uncertainty. If it lies outside of the limits there is no uncertainty, assuming that the limits have been properly determined. If well within the limits either decision will answer, unless other considerations determine the question. And so, although it is not often possible to obtain precise values, we may generally reach a conclusion which is unquestionable. Even under the most unfavorable circumstances the computations, when made with the assistance of all the broad common sense and experience that can be brought to bear, will point to a decision which is much better than mere "judgment," which is responsible for very many glaring and costly railroad blunders. In short, Railroad Economics means the application of systematic methods of work plus experience and judgment rather than a dependence on judgment unsystematically formed. It makes no pretense to furnishing mechanical rules by which all railroad problems may be solved by any one, but it does give a general method of applying principles by which an engineer of experience and judgment can apply his knowledge to better advantage. To the engineer of limited experience the methods are invaluable; without such methods of work his opinions are practically worthless; with them his conclusions are frequently more sound than the unsystematically formed judgments of a man with a glittering record. But the engineer of great experience may use these methods to form the best opinions which are obtainable, for he can apply his experience to make any necessary local modifications in the method of solution. The dangers lie in the extremes, either recklessly applying a rule on the basis of insufficient data to an unwarrantable extent, or, disgusted with such evident unreliability, neglecting altogether such systematic methods of work.