. Graphical and mechanical computation . so that Au = x, Bv = y, Cw = z,Dq = t. Draw vE and qF parallel to AB and CD respectively. Then in the similar triangles vEu and qFw, we haveHence if AX, BY, CZ, DT carry the scales x = «i/i(m), y = mi/j(»),z = m2fz{w), t = m2/4(g), where Wi : kx = mi : &2, then ki = z — t : kz y : k\ = z — t : ki becomes x — y /i(«) ~h(v) =/3(w) -/4(g), and a pair of parallel index lines, (u, v) and(w, g), will cut out values of u, v, w, and qsatisfying this equation. If CZ and DT are drawn perpendicularinstead of parallel to Ax and By, and CDis perpendicular to AB (Fig
. Graphical and mechanical computation . so that Au = x, Bv = y, Cw = z,Dq = t. Draw vE and qF parallel to AB and CD respectively. Then in the similar triangles vEu and qFw, we haveHence if AX, BY, CZ, DT carry the scales x = «i/i(m), y = mi/j(»),z = m2fz{w), t = m2/4(g), where Wi : kx = mi : &2, then ki = z — t : kz y : k\ = z — t : ki becomes x — y /i(«) ~h(v) =/3(w) -/4(g), and a pair of parallel index lines, (u, v) and(w, g), will cut out values of u, v, w, and qsatisfying this equation. If CZ and DT are drawn perpendicularinstead of parallel to Ax and By, and CDis perpendicular to AB (Fig. 496), then apair of perpendicular index lines, (u, v) and(w, q), will cut out values of u, v, w, and q satisfying the equation. To represent the equation fi(u) — f2(v) = f3(w) -f- /4(g), the w- and g-scales must be laid off in opposite directions. If the axes are arrangedin the form of a square, or if the second pair of axes coincide with the firstpair (Fig. 49c) then kx = k2; hence, mi = m2 and all four scales have the. Fig. 49c. 94 same modulusof chart is not NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. IV . Because of the restriction on the choice of moduli, this typea very useful one. We shall only give a single illustration.
Size: 1362px × 1835px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubj, booksubjectengineering