. Graphical and mechanical computation. e need not be graduated. To readthe chart we need two pairs of index lines; the index lines (u, v) and{w, p) intersect in a point on AB, and the index lines {p, g) and {r, s) in-tersect in a point on BC. An example illustrating case (2) is worked out in Art. 41. Case (3). Five variables. fx{u) • /4(g) • J^ir) = ^v) • fz{w). This equa-tion can be written as /i(w) : h{v) = Mw) : p and p : h{q) = h{r) : Iand can be considered as a special form of case (2), where the 5 scale(Fig. 39a) is replaced by a fixed point through which the fourth index linemust pass.

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. Graphical and mechanical computation. e need not be graduated. To readthe chart we need two pairs of index lines; the index lines (u, v) and{w, p) intersect in a point on AB, and the index lines {p, g) and {r, s) in-tersect in a point on BC. An example illustrating case (2) is worked out in Art. 41. Case (3). Five variables. fx{u) • /4(g) • J^ir) = ^v) • fz{w). This equa-tion can be written as /i(w) : h{v) = Mw) : p and p : h{q) = h{r) : Iand can be considered as a special form of case (2), where the 5 scale(Fig. 39a) is replaced by a fixed point through which the fourth index linemust pass. An illustrative example is worked out in Art. 42. Art. 40 TWISTING MOMENT IN A CYLINDRICAL SHAFT 77 We may also chart the equation/i(zO : f-iiv) = fz{w) : p by the methoddescribed in Art. 34, and the equation p = /4(g) -/sW by the first methoddescribed in Art. 32. The arrangement of the scales is shown in Fig. 396,and this arrangement is more compact than that of Fig. 39a, and em-ploys only three index lines instead of four. ^?

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