Returning to Equation (3) which has been plotted in two different ways on page 260, it may be seen that the load that can be hauled up a grade decreases with the per cent of grade very rapidly for the roads having a small coefficient of resistance and very much less rapidly for larger resistances. For example, on steel rails, resistance 10 pounds per ton, μ = ¹⁄₂₀₀, a 1 per cent grade reduces the load to one-third the load that may be hauled on the level, and a 5 per cent grade reduces it to less than one-tenth of the same load. With a good asphalt, brick or concrete road, resistance 20 pounds per ton, μ = ¹⁄₁₀₀, a 1 per cent grade reduces the load to one-half, while a 5 per cent grade reduces it to about one-sixth the load that can be drawn on a level road. While for an earth road in bad condition or a dry sand road, 300 pounds per ton resistance, μ = ³⁄₂₀, a five per cent grade only reduces the level grade load by one-fourth. This shows clearly that the better the road surface the less the grade must be in order to benefit by it. The plots on page 260 show the same thing in different ways, and also that the maximum load that can be hauled with a given force at a constant speed is greater, no matter what the grade, on the better types of roads than on the poorer, but that the very great advantages due to hard roads come with the better type of roads. Incidentally this plot shows that the load that may be hauled, other things being equal, on steel tracks, is very much greater than that that can be hauled on the best hard surfaced road with same power, therefore it will never be possible to haul loads on highways as cheaply as on railways unless the operating expenses on the highways can be made materially less than on railways. [Illustration: Graphical representation of the effect of grade on the load that can be drawn.] [Illustration: Graphical representation of the effect of road resistance on the load that may be drawn.] =Slipperiness.=--Road surfaces which become slippery not only decrease the tractive effort of horses and motors but are very dangerous also. Non-slipperiness ought then to be given weight in the selection of the type of roadway. Observations in London in 1873 by Heywood on slipperiness of pavements indicated granite-block most slippery, then asphalt and wood-block. Greene, in 1885, analyzing a series of observations made in the principal cities of the United States, gave the order of slipperiness as wood-block, granite-block, and sheet-asphalt. Slipperiness increases with grade. A special committee upon road materials of the American Society of Civil Engineers[183] recommend the following maximum grades for various kinds of pavements: