. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . or hump of 6 inches would generally be utterly unnoticed, orat least disregarded. When the ground is very rough and broken it is sometimes I §126. EARTHWOBK. 145 I practically impossible, even with frequent cross-sections, tolocate warped surfaces which will closely coincide with all thesudden irregularities of the ground. In such cases the compu-tations are necessarily more or less approximate and dependencemust be placed on the compensating character of the errors. 126. Appro
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . or hump of 6 inches would generally be utterly unnoticed, orat least disregarded. When the ground is very rough and broken it is sometimes I §126. EARTHWOBK. 145 I practically impossible, even with frequent cross-sections, tolocate warped surfaces which will closely coincide with all thesudden irregularities of the ground. In such cases the compu-tations are necessarily more or less approximate and dependencemust be placed on the compensating character of the errors. 126. Approximate computations from profiles. When apaper location has been laid out on a topographical maphaving contours, it is possible to compute approximately theamount of earthwork required by some very simple and rapidcalculations. A profile may be readily drawn by noting theintersections of the proposed center line with the various con-tours and plotting the surface line on profile paper. Drawingthe grade-line on the profile, the depth of cut or fill may bescaled off at any point. When it is only desired to obtain. Fig. 60. very quickly an approximate estimate of the amount of earth-work required on a suggested line, it may be done by the methoddescribed in § 103, or by the use of Table XVII. But theassumption that the surface of the ground at each cross-sectionis level invariably has the effect that the estimated volumesare not as large as those actually required. The differencebetween the ^4evel section hkms and the actual slope sectionhknq equals the difference between the triangles mon and oqs,and this difference equals the shaded area mpn. The excessvolume is proportional to the area of the triangle mpn. Thisarea may be expressed by the formula, A 0/17 , 7 . r)N2sin^« sin/?cos>5 Area mpn = 2(ib + d cot S) 2 ^—-^. ^ ^ cos 2a —cos 2^ 146 RAILROAD CONSTRUCTION. § 126. The percentage of this excess area to the nominal area Jikmstherefore depends on the dimensions h and
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