(_c_) Car- and locomotive-mileage of equipment operating in Michigan; (_d_) Car- and locomotive-mileage, entire equipment; (_e_) Freight-car mileage of the entire system. The results secured by these different methods show, in many cases, very little difference; all are close, and no injustice is worked by any method, while, in other cases, the figures are widely divergent. The Lake Shore and Michigan Southern Railway owns a high-class main line between Chicago and Buffalo, and for part of the way there are two lines several miles apart; the entire line is double-tracked, and there is much third track. None of this line is located in Michigan, except some 80 miles of single-track main line of the Michigan Division between Toledo and Elkhart. The company, however, has several hundred miles of branch line in Michigan, which comprises most of the branch-line mileage of its system. These lines, generally, are far inferior to its main line. Any apportionment of its equipment between States on the basis of either line-mileage, total track-mileage, or locomotive- and equipment-mileage of total equipment will result in the assignment to Michigan of a value far in excess of a proper or fair amount. An apportionment of locomotive and passenger-car equipment on the basis of equipment-mileage or equipment operating in the State, and for freight cars on the basis of car-mileage of total equipment, was found to be most fair. In making the assignment of values, this study was made for all interstate roads, and such basis used as was apparently most fair in each case, the department making a special effort not to assign to Michigan undue values or those which could not be sustained. _Freight Car Inspection._—One of the most perplexing problems which was faced by the Mechanical Department was the proper and satisfactory inspection and valuation of freight equipment. The freight cars owned by the companies were scattered over the United States and Canada, and the inspection of any considerable percentage of those owned by any company was, of course, an impossibility. The fact that these cars had been purchased in series, so that there were considerable numbers in a group, all of the same age, and built according to the same specifications, made possible a valuation by groups. The acceptance, however, of any arbitrary percentage of depreciation by years, or the acceptance of the rules of depreciation of the Master Car Builders Association, without making independent investigation with a view of establishing the correctness of the rule, appeared to be unwise. The several companies submitted carefully prepared statements of equipment. These statements were compared with the equipment register and the reports to the Commissioner of Railroads. The prices used were those of the rules of interchange of the Master Car Builders Association wherever applicable.