D.—l.

The length in miles for each rate of grade multiplied by the total resistance for that grade and speed, gives the mile-pounds, which is a term that can readily be reduced to foot-pounds or horsepower. Tractive Powee. The tractive power of the Class B locomotive assumed has been computed by the method of my second supplementary report, further investigation having confirmed me in the view, that for the assumed speeds, there is no more satisfactory or accurate way of determining this important factor. Cost of Operation and Maintenance. The elements of cost of operation and maintenance are as follows : Maintenance of way; ventilation of summit tunnel; fuel-consumption ; wages of locomotive-men ; locomotive repairs, renewals, and supplies; car repairs and renewals ; wages of trainmen ; general expense. We will take these up in their order. Maintenance of Way. In Table XIII. will be found the working-expenses of the New Zealand Eailways, classified and distributed in items corresponding to those of the American Interstate Commerce Commission. This table is an aid in computing the effect of rise and fall and of curvature upon various items of maintenance of way, some of which are much more affected thereby than others, while some are not affected at all. The same table shows the per cent, of increase of each item of maintenancecost affected, and the per cent, of increase due to 528 degrees of curvature and a rise and fall of 264 ft. The per cent, affected is taken from " Eailroad Construction, Theory and Practice "by Professor Walter Loring Webb, of the University of Pennsylvania, a revision of Wellington's work on this subject in the light of the large amount of valuable data collected and published by the American Interstate Commerce Commission. The approximate rise and fall and curvature per mile of the New Zealand Eailways, for the year 1901, are known, or have been computed, also the average cost of maintenance of way per train-mile. With these data and the values deduced in Table XIII., the cost of maintenance of way per train-mile for each of the alternate Arthur's Pass lines has been computed by proportion, the results being shown in Table XIV. In Table XIV. has also been introduced the effect of the assistant locomotives on the cost of maintenance of way. The assistant locomotive, according to Webb (page 488), affects repairs to roadway 12-| per cent., and renewals of rails and ties each 50 per cent, per locomotive-mile. This affects the total maintenance of way (656 per cent, of the total operating-cost per mile), 1815 per cent, per locomotive-mile. The helper locomotive runs from Otira to the summit only and return. Therefore, the increased cost of maintenance of way per train-mile over the entire distance between Otira and Bealey will be twice the distance from Otira to summit, multiplied by 18' 15, divided by the distance from Otira to Bealey. The resulting percentage for each line is given in column headed, " Percentage Increase due to Assistant Locomotives " (Table XIV). With the costs of maintenance of way per train-mile from the last column of Table XIV., and the number of train-miles per annum outside of tunnel, the total annual costs in pounds sterling corresponding thereto are found for each of the routes as given in Table XV. The total annual costs in pounds sterling of maintenance of way in tunnel is found as shown by Table XVI. Adding the costs outside to those inside of summit tunnel, we have the total annual cost of maintenance of way in pounds sterling, given in Table XVII., for each line. Ventilation of Summit Tunnel. It is assumed that the summit tunnel of either of the routes would require artificial ventilation on account of its length. With the length of summit tunnel from Table I. and the area of cross-section designed for the Arthur's Pass tunnel of 200 square feet, the formulae for the Saccardo system of ventilation given in my second supplementary report, which system is in successful use in Saint Gothard tunnel and in several others, including the precedents noted in said report, will give the essential elements as shown in Table XXIV. From the last column of Table XXIV. it appears that the tunnel of each route would require practically the same mechanical plant and power to give the required velocity and air-current, provided the ratio of the area of nozzle to the area of tunnel cross-section is properly proportioned. The size of blowers and the horse-power of engine and boiler would be the same as used in my second supplementary report—namely, 200-horse power. The cost of operating such a plant can be safely taken at one-half that for a Class B locomotive for the train-mileage made in the tunnel, except that the wages and general expense would be wholly the same as for a Class B locomotive. The cost of installing the ventilation plant in the case of either of the projected summit tunnels would be fully covered by the provision made in each case by your engineers, as given m the details which have been sent to me. Fue l-consump tion. Authorities do not agree closely on fuel-consumption. Ideas vary according to experience and research. The quality of coal has important bearing, a larger consumption of some coals being required than of others. In the computations of my former reports, 5 lb. of coal was assumed per effective horse-power-hour. This is a figure which is as near correct as can be ascertained for average American practice, but on heavy grades, where a locomotive is working most of the time, with nearly full stroke cut off, it is too low. This is a matter which I have investigated at much length, and am now satisfied that, for conditions such as will be found between Otira and the summit, 6 lb. of coal per effective horse-power-hour should be assumed for these computations. This figure I have recently

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