. Graphical and mechanical computation . %. 1 4 5 Fig. 170. 10 network. The equations of our representing w-curves are of the formxy = mhv, a set of rectangular hyperbolas (Fig. 17a) which are quitedifficult to draw and for which the interpolation is very inaccurate. (2) The equation uv = w can be represented by choosing x = muand y = mw/10 for our two perpendicular scales. The equations of ourrepresenting ^-curves are of the form y = ix/io, a set of radiating straightlines of slope y/10. Fig. 176 illustrates this chart, where u and v varyfrom 1 to 10. The values of v are placed at the end of
. Graphical and mechanical computation . %. 1 4 5 Fig. 170. 10 network. The equations of our representing w-curves are of the formxy = mhv, a set of rectangular hyperbolas (Fig. 17a) which are quitedifficult to draw and for which the interpolation is very inaccurate. (2) The equation uv = w can be represented by choosing x = muand y = mw/10 for our two perpendicular scales. The equations of ourrepresenting ^-curves are of the form y = ix/io, a set of radiating straightlines of slope y/10. Fig. 176 illustrates this chart, where u and v varyfrom 1 to 10. The values of v are placed at the end of the represent-ing lines. For saving of space, the values of w are placed at the points Art. 17 CHARTS FOR MULTIPLICATION AND DIVISION 31 where the horizontals cut the line v = 10 and the rulings above thisdiagonal need not be drawn. Of course, the position of the decimal pointin the value of a variable may be changed with a corresponding changein the result. The great disadvantage of this chart is that the z/-lines. Fig. i7d. converge to a point and also cut the horizontals at very small angles, thusmaking the reading quite inaccurate in parts of the chart. This may beremedied somewhat by rotating the verticals of the scale x = mil throughan angle of 450, without changing the nature of the chart. This is illus-trated in Fig. 17c. In Figs. 17& and 17c, the scale for u can be taken 32 NETWORK OF SCALES Chap. II over a range from o to ioo or, in general, from o to ioh, similarly for therange of v, with corresponding change in the range for w. (3) The equation uv = w can be represented by writing it in theform log u + log v = log w and choosing x = m log u, y = m log v forour two perpendicular scales, , we have the rulings of a sheet of log-arithmic paper. The equations of our representing w-curves are of theform x + y = m log w, a set of parallel straight lines (Fig. iyd). Theseparallel lines are very easily drawn, for the line w = k, for example, cutsu = 1 (or the y-axis) at
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