268 MASSACHUSETTS AGRICULTURE. 



every point on the plans of record. These should never be less 

 than fifty feet, and greater widths must be taken at some points 

 of heavy cutting or embankment ; and, in general, there should 

 be width enough for all purposes of drainage, and preservation 

 of the road-bed, and for obtaining materials for construction and 

 repairs ; except for ballasting, which must often be obtained 

 from gravel beds outside. It is better to have too much than too 

 little. 



Grades. 



There are two general classes of carriages to pass over roads, 

 one for freight, and one for passengers. The former wish to 

 carry the heaviest loads, and the latter to make the best time. 

 Undoubtedly where heavy loads preponderate, there is greater 

 need of light grades, but in general, the road that is best for the 

 one, is the best for the other class of travel. 



We will designate grades in the usual way by a fraction hav- 

 ing unity for the numerator, and the distance required to rise 

 one foot for the denominator ; for the simple reason that this 

 fraction expresses the exact ratio of the draught to the load, as 

 it would be were there no friction. For instance, a grade of one 

 foot in one hundred is called -^Iq, three feet in one hundred 3^3, 

 and five feet in one hundred gV? ^tc. 



It seems to be well established that undulating grades of ^^^r 

 are no detriment, but, on the contrary, are rather beneficial, as 

 giving better longitudinal drainage. 



It is evident, too, that the grade should never exceed the 

 " angle of repose," if possible ; that is, the horse should not be 

 obliged to hold back his load in descent, but the friction should 

 be sufficient to counteract the force of gravity. This " angle 

 of repose," or limit of grade, for different road-beds will vary 

 from -^Q to -Jq- on ordinary roads. It is easily ascertained from 

 the draught upon a level with the same character of surface, 

 for this is just equal to the friction, which would be the same 

 upon an incline. For instance, if the draught upon a level, or 

 what is required to overcome friction, is 2V of load, then this 

 fraction would exactly express the maximum grade to be al- 

 lowed for same kind of surface, since, as stated above, the same 

 fraction gives the ratio of draught to load to overcome gravity 

 alone. So the " angle of repose " is the grade expressed by the 



