This paper is confined to a discussion of the methods which should be used in arriving at a correct figure of cost of reproduction and depreciation—it does not take up questions involving the propriety of those figures when reached. The propriety or legality of using such figures as a basis for an assessed valuation, as a basis for rate-making (rate-making being an art in itself involving complications as great as those encountered in valuation), or any arguments as to the justice or injustice of legislation restricting issues of stocks or bonds, will be conceded no place in this paper. It is assumed that all these questions would have been taken up and a satisfactory answer reached before a valuation could have been ordered. The different elements of value in property, the relations of this property to the public, the method of determining the worth of these elements of value which have been adopted in the past by men engaged on valuation work, a comparison of these methods, a discussion of the objections that have been made to them, and a presentation, not only of the writer's views as to proper methods, but those in which he disagrees with usages adopted by others—these define the scope of this paper. No matter what particular end is to be served by a valuation, the commission engaged upon it will be asked to furnish a fair value, perhaps with reasonable limitations in the instructions, perhaps with a general and indefinite instruction to find the value. They will encounter, among other difficulties: _First._—The fact that human machines are not exact duplicates, and that allowance must be made for a large measure of error, on account of the personal equation of the men engaged on the work, as individual errors of judgment are frequent on any work of magnitude. This personal element must be corrected by uniformity of method, by constant checking, and, as far as possible, by subordination of personality to system. _Second._—The fact that human selfishness is a dominant quality—the railroad manager who opposes methods which he believes will increase values in an appraisal for taxation, or who, on the other hand, uses every possible argument to increase values if the work be as a basis for rate-making or for restriction of bond issues, or the State official who is desirous of using original cost on a valuation to be used for rate-making in order to keep the valuation down to a minimum, and the politician who depends on an unenlightened public opinion to create sufficient outcry to influence the work to his advantage—are all actuated by a perfectly human wish to attain ends which seem to them desirable, and are but typical of men who will endeavor to influence every appraisal. In view of these considerations, it is a question whether results are not frequently affected by the knowledge of their intended use, and whether a system which will entirely remove such causes of error can be applied to the work.