A study of the complete methods of the railroad valuation in Michigan, in connection with these decisions, discloses the fact that they comply with the requirements of the earlier cases, that all matters affecting value be taken into consideration, and that in the more recent decisions the detailed methods adopted in the Cooley physical appraisal have been sustained as to very many points. In no case have any of such methods been unfavorably criticized, and, while at this date the Supreme Court has not squarely passed on the propriety of any method for securing non-physical or intangible values, it has fully sustained the general position of Professor Adams in several important points. In addition to the complete examination of Federal cases, certain very interesting and valuable State cases have been examined, and some of them are quoted. These cases involve both matters of taxation and rate-making. They cover railroads, water-works, gas-works, and other classes of public service corporations, and clearly demonstrate the fact that any analysis of the subject of property valuations must include all classes of corporations. Rate-making and taxation in themselves are entirely separate and distinct from valuation, which is a necessary preliminary step in either undertaking. For this reason all references which are not of special interest in the valuation part of the problem are omitted. The case of Smyth _vs._ Ames (169 U. S., 466) was an action to question the constitutionality of a statute of Nebraska establishing rates. It is of great interest, and, based on the ruling of the Court in this case, the appraiser in Washington and the appraisers in Nebraska have undertaken to secure first cost as an element of value. The decision holds that: (1) A railroad corporation is a person within the meaning of the fourteenth amendment. (2) A State enactment establishing rates that will not admit the carrier to earn such compensation as would be just to it and to the public, would deprive such carrier of its property and would be repugnant to the fourteenth amendment. (3) Rates established by a State cannot be so conclusively determined by the legislature that they cannot become the subject of judicial inquiry. The reasonableness of rates prescribed by a State for intra-state business must be determined without reference to the interstate business done by the carrier or the profits derived from that business. This paper is not concerned with the question of rates, which is discussed at length in this decision. It is, however, of special interest to note what the Court says in regard to the relation of the corporations to the people, and to elements of value.