This value of the “pull” must be diminished by the friction of the locomotive as a machine, by the rolling resistance of the trucks and tender, and by the atmospheric resistance of the locomotive as the head of the train. Prof. Goss proposes the following approximate values for these resistances in a paper read before the New England Railroad Club in December, 1901. A number of tests have shown that a steam pressure of 3.8 pounds per square inch on the piston is required to overcome the machine friction of the locomotive. Hence if _d_ is the diameter of the piston in inches, _L_ the piston-stroke in feet, and _D_ the diameter of driver in feet, while _f_ is that part of the draw-bar pull required to overcome machine friction, the following equation will hold: π_d_² _f_.π_D_ = 3.8 -----× 2_L_ × 2. 4 _d²L_ ∴ _f_ = 3.8 ------. _D_ Again, if _W_ be the rolling load in tons on tender and trucks (excluding that on drivers), and if _r_ be that part of the draw-bar pull required to overcome the rolling resistance due to _W_, then experience indicates that approximately, in pounds, ( _S_ ) _r_ = (2 + --- )_W_. ( 6 ) As before, _S_ is the speed in miles per hour. Finally, if _h_ be that part of the draw-bar pull in pounds required to overcome the head resistance (atmospheric) of the locomotive, there may be written approximately _h_ = .11_S_². The actual draw-bar pull in pounds available for moving the train will then be 375 H.P. _d_²_L ( S_ ) _t = T - f - r - h_ = -------- - 3.8------ - _W_(2 + ----) - .11_S_². _S D_ ( 6 ) The maximum value of _t_ should be taken as one fourth the greatest weight on drivers. If _H_ is the total heating surface in square feet, and if 12 pounds of water be evaporated per square foot per hour, while 28 pounds of steam are required per horse-power per hour, then 12_H_ 375H.P. 161_H_ H.P. = ----- and -------- = ------. 28 _S S_ Hence 161_H d²L_ ( _S_ ) _t_ = ----- - 3.8----- - _W_(2 + ----) - .11_S²_. _S D_ ( 6 ) The actual draw-bar pull in pounds may then be computed by this formula. Some recent tests of actual trains (both heavy and light) on the N. Y. C. & H. R. R. R. between Mott Haven Junction and the Grand Central Station, New York City, a distance of 5.3 miles, by M. Bion J. Arnold, by means of a dynamometer-car, gave the actual average draw-bar pull per ton of 2000 pounds as ranging from 12 to 25 pounds going in one direction and 12.1 to 24 pounds in the opposite direction. There were eight tests in each direction, and the greatest speed did not exceed 30 miles per hour.