. 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
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