. Graphical and mechanical computation . Fig. 34a. AX (Fig. 34&), and where AB is a common transversal. Through anypoint P on AB draw two index lines cutting the axes in the points u, v, w,and q so that Au = x, Bv = y, Aw = z, and Bq = t. How are x, y, z,and t related? From the similar triangles in these figures, we have x : y = AP : PB and z : t = AP : PB, :. x : y = z : t. Now if AX, BY, AZ, BT carry the scales x = mi/i(«), y = m2/2(i>), z = m3f3(w), t = mjiiq), where Wi : w2 = ms : m\, the relation becomes /j («) : /2(y) = f-s(zv) : /4(g)and two index lines intersecting in a point on /15
. Graphical and mechanical computation . Fig. 34a. AX (Fig. 34&), and where AB is a common transversal. Through anypoint P on AB draw two index lines cutting the axes in the points u, v, w,and q so that Au = x, Bv = y, Aw = z, and Bq = t. How are x, y, z,and t related? From the similar triangles in these figures, we have x : y = AP : PB and z : t = AP : PB, :. x : y = z : t. Now if AX, BY, AZ, BT carry the scales x = mi/i(«), y = m2/2(i>), z = m3f3(w), t = mjiiq), where Wi : w2 = ms : m\, the relation becomes /j («) : /2(y) = f-s(zv) : /4(g)and two index lines intersecting in a point on /15 will cut out values oiu, v, w, and q satisfying equation (IV). Hence, to chart equation (IV) f\{u) : fi{v) =fz(w) : Mq) proceed as follows:Through the ends of a segment AB of any convenient length, draw theparallel axes AX and BY and the parallel axes AZ and BT, where AZ Art. 35 PRONY BRAKE OR ELECTRIC DYNAMOMETER FORMULA 69. may coincide or make any convenient angle with AX. On these axesconstruct the scales x = ntifi(u), y = ra2/2(z>), z = m3fs(w), t = mif4(q) where the moduli are arbitrary except for the relation nti : m2 = m3 : read the chart, use twoindex lines, one joining uand v, and the other join-ing w and q, and intersect-ing in a point on AB. The following examplesillustrate this type of chart: 35. Prony brake orelectric dynamometer ( . „„ 2TTLNW formula, = . 33,000 for measuring the power of a rotating shaft. Either the prony brake or the electric dynamometer may be used. With such an arrangement the power is given by the above formula, where L is the length of brake arm in feet, N is the speed of the shaft in revolutions per minute, and W is the load on scale in pounds. If we write the equation as W A7 ? = —??—tt , we have an equa-N 5260/L M tion of the form (IV), and our scales are x = , y = m2N, 5260 Fig. sketch in Fig. 35a gives the method KALEVI
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