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added advantage affected applied approx approximation arranged base breaks calculation centre cloth cols column combining computation connected considered constructed containing convenient correction corresponding cross-sections diagram difference dist distance divide earthwork elev entire equal error estimate example excavation expression extend factors final former formula grade greater half height Henck illustrated important included interm irreg labor last interm latter length manner measurements method moving multiplied notes obtain once operation original plane position pris prismoidal prods Prof quantities remaining represent respective result ridges rule seen shape shown side similar single slope stas subtraction supposed surface line taken term third tion triangle true values vanishing volumes warped whole widths zero
Página 8 - Sb(mid-widths + ^ end-widths) >• • . — 2Sb2 x no. of vols. } 54 Let us illustrate this formula by applying it to the following extract from a field book, containing columns of stas., centre cuts, left and right heights and dists. of slope-stakes, the road-bed being 18 ft., slope, 1 to 1, dist. apart of stas., 100 ft.: EIGHT.
Página 8 - ... represent width and centre at next station, the area of its cross-section may be expressed by a formula similar to the above : half the sum of these, multiplied by dist., D, between, and divided by 27, gives a near approximate of the volume bet. in cu. yds. B@- Vol. - (we+w'c1 + Sb(w + iu')-4:SI?)T™Add two consecutive volumes of equal length by means of the general formula, w",c", representing the width and centre of third cross-section : Vol. = (we + 2w/c' + w"c" + Sb(w + 2w/ + iv") - SSff)^.
Página 8 - Supposing w', c' to represent width and centre at next .station, the area of its cross-section may be expressed by a formula similar to the above : half the sum of these, multiplied by dist., D, between, and divided by 27, gives a near approximate of the volume bet. in cu. yds.
Página 8 - By continual addition we may get a formula. for the sum of any number of consecutive volumes ; but, letting n denote the number of volumes, we may at ouce indite a general formula for the calculation of any number of volumes consecutive.