. Graphical and mechanical computation . atevalues of n we interpolate between twocurves. Fig. 606 gives the complete chart forthe equation w3 + nw2 + pw -\- q = to solve this equation, we draw the index line joining p and q;this cuts the w-curve in the required root. To find negative roots, andto find the roots when p and q lie beyond the limits —10 and +10, weproceed as in the case of the simple cubic w3 -f- pw + q = o. Example 4. Solve the equation w3 + w2 — w — = o. Theindex line joining p = — and q = — cuts the curve n — 1 inw> = Example 5. Solve the equation
. Graphical and mechanical computation . atevalues of n we interpolate between twocurves. Fig. 606 gives the complete chart forthe equation w3 + nw2 + pw -\- q = to solve this equation, we draw the index line joining p and q;this cuts the w-curve in the required root. To find negative roots, andto find the roots when p and q lie beyond the limits —10 and +10, weproceed as in the case of the simple cubic w3 -f- pw + q = o. Example 4. Solve the equation w3 + w2 — w — = o. Theindex line joining p = — and q = — cuts the curve n — 1 inw> = Example 5. Solve the equation w3 + 96 w2 + w — 7, o (this equation occurs in the problem of the equilibrium of arches).If we let w = aw = 10 w, the equation becomes w3 -f- w2 + w— = o and the index line joining p = and q = — cuts thecurve n = in w = Hence w = We can similarly plot alignment charts for any trinomial equationwm + pwn + 2 = o and for the fourth degree equation w4 + nw2 +pw + q = U4 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. v (XI) ADDITIONAL FORMS OF EQUATIONS. COMBINED METHODS.* 61. Chart for equation of form + /4O) . — This form /i(u) Hv) Hw)is a generalization of equation (IX). Consider two intersecting axes AXand AY and a curved axis CZ (Fig. 61). Let any transversal cut theaxes in u, v, and w respectively, and draw wD parallel to A Y, so thatAn = x, Bv = y, AD = x, and Dw = 2. Then in the similar triangles,uDw and nAv, we have Dw : Av = Dit : An, or
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