Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 ...AE perpendicular to OD, cutting OZ in E. Then OA + OB Art. 21 HEXAGONAL CHARTS 41 Thus, if the axes OX, OY, OZ carry the scales x = mf(u), y = mF(v), t(w) respectively, then the three perpendiculars from any point thus, any equation of this type may be represented by three scales. The indices h, 72,-3 may be drawn on a transparent sheet and this sheet is Fig. 2id.. moved over the paper keeping the indices perpendicular to the axes. Fig. 21c charts the equation----=--by this method. u v w We can choose the modulus on OZ the same as the moduli for OX and OY by following the construction illustrated in Fig. 216. Here OX and OF cut at an angle of 1200 and OZ bisects this angle. Join OP and let angle COP = a. Then OA = OP cos (6o + «) = OP (cos 6o cos a-sin 6o sin a). OB = OP cos (6o-a) = OP (cos 6o cos a + sin 6o sin a)..-. 0/1 + 05 = 2 OP cos 6o cos a = OP cos a = OC. Thus our three scales are x = mf(u), y = mF(v), z = mp(w). Fig. 21d charts the equation «t = «/or log M + log v = log w by this method. EXERCISES. i. Represent the equation v = it3 by a straight line, using natural scales. 2. Represent the equations (a) 2 u2 + 3 i = 6, (b) u2--3 i2 = 1, (c) u2 4-fl2 = 4 by straight lines, using natural scales, and find graphically the simultaneous solutions of the three equations taken in pairs. «t 3. Find graphically the simultaneous solutions of the equations v = 6 e 16 and v = 10 e. _i£ 4. Solve graphically the equation u = be ". 5. Construct a sheet of logarithmic coordinate paper and draw on it the straight lines representing the (a) v = u3; (b) v (c) v = (d) C = ir£ (circumference of circle); (e) A =-.D2 (area of circle); (f) pv1-41 = 2 (adiabatic expansion of a gas); 4 D2 U2 (g) A =--= T--(h = velocity head in ...
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