. Graphical and mechanical computation. Fig. 320. Fig. 32&. index line cutting the axes in the points u, v, w so that Au = x, Bv = = 2; note that Au and Bv are oppositely directed. How are x,y, and z related? Let AB = k. Then in the similar triangles Auw and Bvw, Au : Bv = Aw : wB, or x : y = z : k — z, or x = k — z :y- Now if AX and 5F carry the scales x = mifi{u) and y = m<ifi{v), the last equation becomes /i(m) = —.,_ , h{v), and if AZ carries a scale for w such that 71 r = jz{w) or z = k —^ .• , 1 mi{k - z) -^ ^ mjiiw) + TTH 66 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. IV the equat
. Graphical and mechanical computation. Fig. 320. Fig. 32&. index line cutting the axes in the points u, v, w so that Au = x, Bv = = 2; note that Au and Bv are oppositely directed. How are x,y, and z related? Let AB = k. Then in the similar triangles Auw and Bvw, Au : Bv = Aw : wB, or x : y = z : k — z, or x = k — z :y- Now if AX and 5F carry the scales x = mifi{u) and y = m<ifi{v), the last equation becomes /i(m) = —.,_ , h{v), and if AZ carries a scale for w such that 71 r = jz{w) or z = k —^ .• , 1 mi{k - z) -^ ^ mjiiw) + TTH 66 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. IV the equation becomes/i(i<) = f2(v) Mw), and any index line will cut theaxes in three points corresponding to values u, v, w satisfying this equa-tion. Hence, to chart equation (III) fi{u) = Mw) - fiiv) proceed as follows:Draw three axes AX, BY, and AZ, where AX and BY are parallel andoppositely directed, and AB is any convenient length, k. With A andB as origins, construct on these axes the scales Note that for the construction
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