. Graphical and mechanical computation. given in the text are those which were employed originally in theconstruction of the scales; these values do not however refer to the cuts which, in mostcases, are reductions of the original drawings. Art. 3 VARIATION OF THE SCaLE MODULUS function with moduli mi, nto, ms, . . , respectively. Only one of thesescales need be constructed by means of a table of values of/(m), and theothers may be derived graphically from this. In Fig. 3a, let OiXi carry the scale Xi = mif{u); we wish to constructthe scale X2 = mof{u). Let 0 be any con-venient point; join OOi
. Graphical and mechanical computation. given in the text are those which were employed originally in theconstruction of the scales; these values do not however refer to the cuts which, in mostcases, are reductions of the original drawings. Art. 3 VARIATION OF THE SCaLE MODULUS function with moduli mi, nto, ms, . . , respectively. Only one of thesescales need be constructed by means of a table of values of/(m), and theothers may be derived graphically from this. In Fig. 3a, let OiXi carry the scale Xi = mif{u); we wish to constructthe scale X2 = mof{u). Let 0 be any con-venient point; join OOi and on this linechoose O2 such that OO2/OO1 = milmx\through O-i draw 02-^2 parallel to 0\Xx. Ifi4 is a point on OxX\ marked u\ then 0\A =*Wi/(m). and OA will cut O1X1 in a point B X, X2 such that OiBjOxA OO2/OO1 or O2B = — mi B o, inif{u) = ntofiu), and thus B will also bemarked u. By joining 0 with all the pointsA of the scale OiXi we shall thus get thepoints B of the scale O2X2 so that corresponding points on the- same Fig. OS Fig. 36. SCALES AND THE SLIDE RULE Chap. 1 transversal through O will be marked with the same value of u, andthe scale on 02^2 will have for its equation X2, = ni2f{u). The transversals through 0 need not be drawn, but simply theirpoints of intersection with 02^2 indicated. If the transversals through0 are drawn, then we may get a scale of any required modulus by merelydrawing a parallel to 0\Xi dividing the segment OOi in the required ratio;thus a line midway between 0 and Oi will carry a scale with modulusgraphicalmechani01lipk
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