The theory of grades is somewhat different when motor vehicles are considered, since it is allowable to permit considerably higher speed than with horse drawn vehicles before applying the brakes and the effect of grade can be utilized not only in translating the vehicle down the grade, but also in overcoming resistances due to mechanical friction and the air. On long grades, a speed might be attained that would require the use of the brake or the same condition might apply on very steep short grades. There is at present insufficient data on the tractive resistance and air resistance with motor vehicles to permit the establishing of rules relative to grade, but experience indicates a few general principles that may be accepted. If a hill is of such rate of grade and of such length that it is not necessary to use the brake it may be assumed that no energy loss results so far as motor vehicles are concerned. Where there is no turn at the bottom of the hill and the physical condition of the road permits speeds up to thirty-five or forty miles per hour grades of five per cent are permissible if the length does not exceed five hundred feet and grades of three per cent one thousand feet long are allowable. It is a rather settled conviction among highway engineers that on trunk line highways the maximum grade should be six per cent, unless a very large amount of grading is necessary to reach that grade. =Undulating Roads.=--Many hills exist upon highways, the grade of which is much below the maximum permissible. If there are grades ranging from 0 to 4 per cent, with a few hills upon which it is impracticable to reach a grade of less than six per cent, it is questionable economy to reduce the grades that are already lower than the allowable maximum. It is especially unjustifiable to incur expense in reducing a grade from two per cent to one and one-half per cent on a road upon which there are also grades in excess of that amount. The undulating road is not uneconomical unless the grades are above the allowable maximum or are exceptionally long or the alignment follows short radius curves. =Safety Considerations.=--On hills it is especially desirable to provide for safety and curves on hills are always more dangerous than on level sections of road. Therefore, it is desirable to provide as flat grades as possible at the curves and to cut away the berm at the side of the road so as to give a view ahead for about three hundred feet. Whether a road be level or on a hill, safety should always be considered and the most important safety precaution is to provide a clear view ahead for a sufficient distance to enable motor vehicle drivers to avoid accidents. [Illustration: Fig. 9.--Types of Guard Rails]