GRADING OF ROADS. 269 



fraction wliicli indicates the ratio of draught to load upon the 

 same road-bed on a level. 



Very many experiments have been made in Europe to find 

 this ratio upon every variety of surface, and we have full tables 

 of the results. We will only state briefly that upon such roads 

 as we shall have in Massachusetts, varying from those of earth 

 and gravel mixed, to those of broken stone, in good order, ac- 

 cording to these data, the draught would range from -^ to -^^ of 

 load on a level. Now, theoretically^ to find the power required 

 upon any given grade, we have only to add to this the ratio of 

 perpendicular rise to length of surface, i. e, the fraction ex- 

 pressing the grade. For instance, if the power on a level, with 

 the same road-bed, is 3^^ of load, on a grade of 2V ^^^^ power 

 required would be tj o'^2V=tV ^^ load. But, practically^ this 

 calculation for power required on grades from that on a level 

 would lead to wrong conclusions, for a horse does not pull at so 

 great advantage on an incline, on account of the position of his 

 body, not being able like a man, to throw the centre of gravity 

 forward at his will, and not having so good foothold, and the 

 load, too, being thrown more upon the hind wheels, there would 

 be increase of friction on a yielding surface. So we must resort 

 to experiment again, as upon a level ; and the general results 

 are, that a horse can haul about ^ as much on a grade of -g^^ as 

 on a level ; | as much on a grade of -^^ ; -| on a grade of 2V ; 

 and only \ as much on a grade of J^ as on a level. 



These are condensed general statements from English and 

 French experiments ; but the State should at once institute full 

 experiments upon her own roads, with the vehicles in com- 

 mon use, and with such as shall prove the best. 



Now the maximum grade upon any line being fixed from such 

 considerations as have been named, it still remains a question of 

 great importance how much you will increase the distance, or 

 the cost, to reduce grades that are within the prescribed limits. 

 No special rules for each case can be laid down, but they are 

 questions for the engineer on the ground, in view of all the facts 

 and principles that should control the decision. We will men- 

 tion a few general rules that are well established. 



1. The capacity of a line of road should not be limited by 

 a portion which is a small percentage of the whole. If possible, 

 let the greatest load that can be drawn up the steepest part be a 



