The Civil engineer and architect's journal, scientific and railway gazette . On Tables for Setting out the Width of Cuttings and Embankmentson Sidelong Ground; and also Formulce for Computing the Area ofVertical Section. By R. G. , The object of this paper is to investigate some simple formula?,and from thence to construct some tables, to enable the assistantengineer or contractor to set out the widths of cuttings and em-bankments on sidelong ground; and also to calculate the solidcontent of any portion of the ground. The subject may be re-solved in the following proposition:— Given
The Civil engineer and architect's journal, scientific and railway gazette . On Tables for Setting out the Width of Cuttings and Embankmentson Sidelong Ground; and also Formulce for Computing the Area ofVertical Section. By R. G. , The object of this paper is to investigate some simple formula?,and from thence to construct some tables, to enable the assistantengineer or contractor to set out the widths of cuttings and em-bankments on sidelong ground; and also to calculate the solidcontent of any portion of the ground. The subject may be re-solved in the following proposition:— Given the / of inclination of ground, the depth (from field-book, &c.) of ground to the centre of balance or formation level,and tlie ratio of the slopes; to determine where they will meet theground at surface. Let HAFBD (fig. 1) be a vertical section of the ground;A B the formation line, represented by 2 i ; the given angle of in-clination of ground H D with the horizon by e ; tlie given depthO F from the stake O perpendicular to centre of formation leveldenoted by F B Fig. i. I. We will proceed first to determine a formula for O D Let ; draw DK perpendicular to A B produced ; O/parallel toA B K Let D B be the given slope m base to 1 perpendicular ;draw the vertical B C. Let D/= y; then Oc = FB = 6; ef= my; also by similartriangles, C e ;= m a. .??Of=b + ma + , by triangle O/D, right-angled at/, we haveI : x :: sine : y. .? .g =, 1 : x :\ cos e : b + 7na + my. . cose =z b -{? ma -\- , then x (cos e - msiae) = b + ma ;b -\- ma therefore, a? =1 (1) of the above formula, the Table From the factor, — cos 8 — m sin f No. I. is computed from 5° to 20°. 2. To find an expression for O H measured from O on thedescent. Draw H M (fig. 2) perpendicular to A B produced. Let H A be r 0 ^g0f^ 5 Fig. 2. the given slope, ratio as before. Let H M = ?/; then will A M =: m y. Therefore, H G = N F = 6 -(- nj«/; also O g ^ a — y. By the triangle
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