class="tdcenter">10-34 E

" Lehigh Valley, Wyoming Div. A. Mitchell, Div. Supt. 1871 Baldwin Catalogue, 1881, p. 112   19 12.0 0.022     850 74 175 156 0.166 D-D 16 " Great Northern Grafton Greenough. 1908 Baldwin Loco. Wks. Record, No. 65, p. 29   20 13.0 0.022     800 74 177 158 0.153 D-D 1 " Great Northern Grafton Greenough. 1908 Baldwin Loco. Wks. Record, No. 65, p. 29   21 13.0 0.022 14°   415 50 91 83 0.154 Consol. " Baltimore & Ohio F. E. Blaser, Div. Supt. 1910   Very crooked line. Uncompensated. 22 16.0 0.0044     950 30 51 44 0.164 10-34 E " Central of N. J. W. W. Stearns, Asst.Gen.Supt. 1880 Baldwin Catalogue, 1881, p. 113   23 20.0 0.022     500 62 97.5 90 0.170 F 8, Consol. " Great Northern Grafton Greenough. 1908 Baldwin Loco. Wks. Record, No. 65, p. 29   24 20.0 0.022     800 74 177 158 0.159 L-1, Mallet. " Great Northern Grafton Greenough. 1906 Baldwin Loco. Wks. Record, No. 65, p. 29  

In proportioning grade resistance for any line, therefore, a locomotive may be counted on to utilize 24.3% of the weight on the drivers for a distance of 5 miles on a 0.002 grade without any assistance from momentum, and, in the event of an unexpected stop, should be able, as soon as a full head of steam is built up, to start the train and carry it over the grade. This is probably a maximum, considering the condition of the equipment of this Virginian Railway, as previously mentioned.

Treating Item 14 in the same way, a distance of 2,310 ft. is accounted for by momentum, leaving, say, 5.5 miles for the steam, or the length of a 0.02 grade on which a locomotive may be loaded on a basis of tractive power equal to 24.2% of the weight on the drivers.

From these figures it may be concluded that on lines having grades from 12 to 15 or more miles in length, grades of 3 to 5 miles in length may be inserted having rates 50% in excess of that of the long grades, without decreasing the capacity of the line. This statement, of course, is general in its bearings, each case being subject to its especial limitations, and subject to detailed calculations.

It may be noted that the velocity of 60 ft. per sec., assumed at the foot of the grade, is probably higher than should be expected in practice; it insures, on the other hand, that quite enough has been allowed for momentum, and that the results are conservative.

Arguments like the foregoing are always more or less treacherous; being based on statistics, they are naturally subject to material modifications in the presence of a larger array of data, therefore, material assistance in reaching practical conclusions can be given by the presentation of additional data.

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DISCUSSION

C. D. Purdon, M. Am. Soc. C. E. (by letter).—Some years ago the writer, in making studies for grade revision, found that the tractive power of a locomotive up grade becomes less as the length of the grade increases, and in some unknown proportion. This was a practical confirmation of the saying of locomotive engineers, that the engine "got tired" on long grades. On a well-known Western railroad, with which the writer is familiar, experiments were made for the purpose of rating its locomotives. The locomotives were first divided into classes according to their tractive power, this being calculated by the usual rule, with factors of size of cylinders, boiler pressure, and diameter of drivers, also by taking one-fourth of the weight on the drivers, and using the lesser of the two results as the tractive power.

Locomotives of different classes, and hauling known loads, were run over a freight division, the cars being weighed for the purpose; thus the maximum load which could be handled over a division, or different parts of a division, was ascertained, and this proportion of tonnage to tractive power was used in rating all classes.

Of course, this method was not mathematically accurate, as the condition of track, the weather, and the personal equation of the locomotive engineers all had an effect, but, later, when correcting the rating by tests with dynamometers, it was found that the results were fairly practical.

There were three hills where the rate of grade was the same as the rest of the division, but where the length was much in excess of other grades of the same rate.

Designating these hills as A, B, and C, the lengths are, respectively, 2.44, 3.57, and 4.41 miles. There were no other grades of the same rate exceeding 1 mile.

In one class of freight engines, 10-wheel Brooks, the weight of the engine was 197,900 lb.; tender, 132,800 lb.; weight on drivers, 142,600 lb.; boiler pressure, 200 lb.; and tractive power of cylinders, 33,300 lb.

On Hill A these engines are rated at 865 tons, as compared with 945 on other parts of the division. As the engine weighs 165 tons and the caboose 15 tons, 180 tons should be added, making the figures, 1,045 and 1,125 tons. Thus the length of the grade, 2.44 miles, makes the tractive power on it 92% of that on shorter grades.

On Hill