. Graphical and mechanical computation . ga Art. 49 CHART FOR EQUATION (VII) 93 Consider a pair of parallel axes AX and BY, k\ inches apart, and an-other pair of parallel axes CZ and DT, k2 inches apart, parallel to the firstpair; AB and CD are also parallel. (Fig. 49a.) Draw two parallelindex lines, one intersecting AX and BY and the other intersecting CZ. I I -/- -^jY X Fig. 49a. Fig. 49&. and DT in u, v, w, and q respectively, 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 ca
. Graphical and mechanical computation . ga Art. 49 CHART FOR EQUATION (VII) 93 Consider a pair of parallel axes AX and BY, k\ inches apart, and an-other pair of parallel axes CZ and DT, k2 inches apart, parallel to the firstpair; AB and CD are also parallel. (Fig. 49a.) Draw two parallelindex lines, one intersecting AX and BY and the other intersecting CZ. I I -/- -^jY X Fig. 49a. Fig. 49&. and DT in u, v, w, and q respectively, 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
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