. Railroad construction. Theory and practice . Fig. 47. As this method of cross-sectioning implies considerable approxi-mation, it is generally a useless refinement to attempt to com-. FiG. 48. § 74. EARTHWORK. 83 pute the voiume with any greater accurac}^ than that obtainedby averaging end areas. It may be noted that it may be easilyproved that the correction to be appHed is of the same form asthat foimd in § 71 and equals j^[(a-/ + xr) -{xi + Xr)] [(.d + a) -{d + a)l which reduces to When d =d the correction vanishes. This shows that whenthe center heights are equal there is no correction—re
. Railroad construction. Theory and practice . Fig. 47. As this method of cross-sectioning implies considerable approxi-mation, it is generally a useless refinement to attempt to com-. FiG. 48. § 74. EARTHWORK. 83 pute the voiume with any greater accurac}^ than that obtainedby averaging end areas. It may be noted that it may be easilyproved that the correction to be appHed is of the same form asthat foimd in § 71 and equals j^[(a-/ + xr) -{xi + Xr)] [(.d + a) -{d + a)l which reduces to When d =d the correction vanishes. This shows that whenthe center heights are equal there is no correction—regardlessof the slope. If the slope is uniform throughout, the form of thecorrection is simplified and is invariably negative. Under theusual conditions the correction is negative, , the methodgenerally gives too large results. 74. Level sections. AMien the country is very level or whenonly approximate preliminary results are required, it is some-times assumed that the cross-sections are level. The method oflevel sections is capable of easy and rapid computation. Thearea may be written as (a + d)^s-^ (50) ! / ■ iiiii^iimiiiiiiiiimim\ I / \ Fig. 49. 1
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