. Graphical and mechanical computation . Fig. 45a. Fig. 456. coincides with AX and BT is either parallel to or coincides with A Y,(Figs. 45a, b). Draw two parallel index lines, one meeting AX and A Y,and the other meeting BZ and BT in 11, v, w, and q respectively, so that 88 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. IV Au = x, Av = y, Bw = z, and Bq = t. Then, in the similar trianglesuAv and wBt, we have x : y = z : t. Hence if AX, A Y, BZ, BT carrythe scales x = mi/i(w), y = nhftiv), z = ra3/3(w), / = ra4/4(g),respectively, where m\ : m% = m3 : ra4, then x : y = z : t becomes fi(u) : /a(i>) =
. Graphical and mechanical computation . Fig. 45a. Fig. 456. coincides with AX and BT is either parallel to or coincides with A Y,(Figs. 45a, b). Draw two parallel index lines, one meeting AX and A Y,and the other meeting BZ and BT in 11, v, w, and q respectively, so that 88 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. IV Au = x, Av = y, Bw = z, and Bq = t. Then, in the similar trianglesuAv and wBt, we have x : y = z : t. Hence if AX, A Y, BZ, BT carrythe scales x = mi/i(w), y = nhftiv), z = ra3/3(w), / = ra4/4(g),respectively, where m\ : m% = m3 : ra4, then x : y = z : t becomes fi(u) : /a(i>) = f3(w) :/4(g), which is equation (VI), and a pair of parallel index lines, («, v) and (w, g)will cut out values of u, v, w, and q satisfying this equation. A pair ofcelluloid triangles will aid in reading the chart. Consider again two pairs of intersecting axes AX, AY and BZ, BTso constructed that BZ is perpendicular to AX and BT is perpendicularto A Y (Figs. 45c, d). Draw two perpendicular index lines, one meeting. Z Y N WM u X, T q- ^L / X / \ \ \ Fig. 45c. A Fig. 45</. AX and AY and the other meeting BZ and BT in u, v, w, and q re-spectively, so that Au = x, Av = y, Bw = z, and 5g = /. Then againx : y = z : t, and if our axes carry the scales described above, a pair ofperpendicular index lines, (u, v) and (w, q), will cut out values of u, v, w,and q satisfying equation (VI). A sheet of celluloid with two perpen-dicular lines scratched on its under side will aid in reading the chart. If the equation involves only three variables, , f\(u) = f2(v) -^(w),the equation can be written /i(w) : f2(v) = /3(w) : 1; here the g-scale isreplaced by a fixed point through which the second index line must alwayspass. It is evident that there are other positions for the axes than thoseillustrated in Figs. 45a, b, c, d that will satisfy the conditions imposed bythe problem. Art. 46 WEIGHT OF GAS FLOWING THROUGH AN ORIFICE »9 46. Weight of gas flowing through an orifice. TT CpV TT tv =
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