. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . y lower-ing the grade line near that place, and diminish the cut (andhence the amount of material to be wasted) by raising thegrade line at or near the place farther on. Whether the advan-tage thus gained would compensate for the possibly injuriouseffect of these changes on the grade line would require patientinvestigation. But the method outlined shows how the mass 162 RAILROAD CONSTRUCTION, §136. curve might be used to indicate a possible change in grade Hnewhich might be dem
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . y lower-ing the grade line near that place, and diminish the cut (andhence the amount of material to be wasted) by raising thegrade line at or near the place farther on. Whether the advan-tage thus gained would compensate for the possibly injuriouseffect of these changes on the grade line would require patientinvestigation. But the method outlined shows how the mass 162 RAILROAD CONSTRUCTION, §136. curve might be used to indicate a possible change in grade Hnewhich might be demonstrated to be profitable. 136. Limit of free haul. It is sometimes specified in con-tracts for earthwork that all material shall be entitled to freehaul up to some specified limit, say 500 or 1000 feet, and thatall material drawn farther than that shall be entitled to anallowance on the excess of distance. It is manifestly imprac-ticable to measure the excess for each load, as much so as tomeasure the actual haul of each load. The mass diagram alsosolves this problem very readily. Let Fig. 65 represent a pro-. FiG. 65. file and mass diagram of about 2000 feet of road, and supposethat 800 feet is taken as the limit of free haul. Find two points,a and h, in the mass curve which are on the same horizontal lineand which are 800 feet apart. Project these points down to aand h\ Then the cut and fill between a and ¥ will just balance,and the cut between A and a will be needed for the fill betweenV and C. In the mass curve, the area between the horizontalline ah and the curve aBh represents the haulage of the materialbetween a and 6, which is all free. The rectangle dbmn repre-sents the haulage of the material in the cut A^a across the 800feet from a to h\ This is also free. The sum of the two areasAam and hnC represents the haulage entitled to an allowance,since it is the summation of the products of cubic yards timesthe excess of distance hauled. If the amount of cut and fill was
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