A somewhat unusual solution of a problem in pusher grades is given by the possibility of using two pusher-engines on some grades and one pusher-engine on correspondingly lower grades. Working out such a method on the basis of the engine previously considered, and assuming that the 1.9% grade is the grade for two pusher-engines, we might determine the corresponding grades for one pusher and for through engines as follows:

Tractive power of three engines = 106,000 x 9/40 x 3 = 71,550 pounds. Resistance on 1.9% grade = 6 + (20 x 1.9) = 44 lbs. per ton 71,550 / 44 = 1626 = gross load in tons. 1626- (3 x 107) = 1305 = net load in tons. 1305+(2 x 107) = 1519 = gross load on the one-pusher grade. Tractive power of two engines = 47,700 lbs. 47,70 / 1519 = 31.40 = possible tractive force in lbs. per ton. (31.40 - 6) / 20 = 1.27% = permissible grade for one pusher. 1305+107 = 1412 = gross load on the through grade. Tractive power of one engine = 23,850 lbs. 23,850 / 1412 = 16.89 = possible tractive force in lbs. per ton. (16.89-6) / 20=0.54%=permissible through grade.

On account of its simplicity the above problem has been worked out on the basis that the normal tractive resistance is uniformly six pounds per ton, and also that the normal adhesion of the drivers is 9/40 On the basis of these figures the grades for one, two, and three engines are precisely as given above. Using other types of engines and assuming other values for the resistance and adhesion, the relation of these grades will change somewhat, although, as shown in the following tabular form, the variation will be but slight.

## Table XXX. Relation Of One-Pusher And Two-Pusher Grades To Through Grades, With Variations Of The Ratios Of Adhesion And Normal Resistance

 Adhesion of drivers. Resistance per ton. Load on drivers. Through grade. One-pusher grade. Two-pusher grade. 1/5 6 lbs. 53 tons. .54% 1.26% 1.86% 1/5 7 " 53 " .54 1.29 1.92 9/40 6 " 53 " .54 1.27 1.90 9/40 7 " 53 " .54 1.31 1.96 1/4 6 " 53 " .54 1.28 1.93 1/4 7 " 53 " .54 1.32 2.00