D.—l.

used in connection with an important line in Colorado, and am now using in a report on the merits of certain routes across the Sierra Nevada Mountains, in California and Nevada, for a transcontinental line. We can now compute the fuel-consumption required by each route, directly from the total resistance pertaining thereto, thus eliminating many details which entered into the computations of my previous reports, as follows : — Multiplying the total resistance in pounds by the distance in feet through which it operates, will give the foot-pounds of effective work done in moving the train. For each hour, this would be the resistance in pounds multiplied by 5,280 and by the speed in miles per hour. Dividing the latter product by 33,000 (foot-pounds) and by 60 (minutes) gives the effective horse-power expended. This quotient multiplied by the running-time in hours and by 6 lb. of coal per effective horse-power hour gives the total coal consumed in pounds. Expressing this in an equation, we have— —^—I^7^—tL—-— = coa l consumed in pounds, where E is the total resistance in pounds. ooLHXJ X oO The speed S is equal to the distance in miles M divided by the running-time H in hours : S = =sr. Substituting this value of Sin the above equation the term H cancels out and we have— B x 5280 x M x 6 3300Q xgo = c °al consumed m pounds. Dividing by 2,240 to reduce the results to tons and multiplying by the cost of coal (in this case £065) will give the cost of coal in pounds sterling : — BX M X 6380 x 6;>.'65 BM = cogt f f j . & t j. 33000 x 60 x 2240 2153846 F s Then, dividing the total resistance in mile-pounds of Tables 11. to IX. inclusive by 215,384-6 gives the cost of fuel for a round-trip train in pounds sterling. Table X. gives the number of train and locomotive miles in summit tunnel and outside of summit tunnel and the total between Otira and Bealey for one round-trip train, and Table XI. shows the average daily mileage of assistant locomotives for each line with 500, 700, 1,000, 340, 477, and 681 trains per annum in each direction, the train-mileage being assumed as equally distributed over 312 working-days. The costs of fuel per round-trip trains, as given in Tables 11. to IX. inclusive, are then multiplied by the total number of round-trip trains per annum, giving the total annual cost of fuel for locomotives of each route and number of trains per annum. These results are shown in Table XII. Wages of Locomotive-men. These are based upon the rates established in New Zealand as measured by the locomotivemile (see New Zealand Eailways Eeport for 1901), the cost per locomotive-mile being 4'18d., assumed to be the same for any locomotive on either route. Locomotive Repairs, Renewals, and Supplies. Taking the costs per locomotive-mile of locomotive repairs, renewals, and supplies for Class B locomotives from the New Zealand Eailways Eeport of 1901, page 62, which are the average of 125,524 engine-miles, we have the distribution shown in the first column of Table XX. The rates per locomotive-mile for an 85-ton locomotive would be greater. According to Wellington and Webb, the items should increase about one-half as fast as the increase in weight, that is, if the total weight of the locomotive is doubled, the cost of renewals and repairs and supplies would increase about 50 per cent. Therefore, if E is the cost of one of these items for class B locomotive, the cost for an 85-ton locomotive will be— R1 = R ( 1 + = R xl= Lls4R - Table XVIII. shows the effect of rise and fall and curvature on the cost of repairs and renewals and supplies per locomotive-mile, obtained in the same manner and with the same reasoning as was used in finding the effect of these physical characteristics on costs of maintenance of way and equipment. These rates per locomotive-mile from Table XVIII. are shown in Table XX. for Class B locomotive, and for the 85-ton locomotive the rates for the Class B locomotive are multiplied by 1.154 (see above equation), giving the results shown in Table XX. With the number of locomotive-miles per round-trip train from Table X., and the rates from Table XX., we obtain the costs for one round-trip train as shown in Table XXI. Multiplying the costs per round-trip train by the number of trains per annum gives the total annual charge for locomotive repairs, renewals, and supplies, see Table XXI. Following the same method as used in my first and second supplementary reports, a day's work for an assistant locomotive is assumed to be eighty miles, and the difference between eighty miles and the actual average daily mileage is called the potential mileage, and is an item of the total cost of motive power. The cost for this potential mileage will be taken as before at the total cost of wages per locomotive-mile plus 10 per cent, of the cost of all the other items. For the Class B locomotive this amounts to 5'15d., and for the 85-tou locomotive s'3od. Multiplying these rates by 80 miles, less the actual mileage of assistant locomotives per day for each line and number of

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