. Graphical and mechanical computation . tangents at Bo, B\, B2, . Xi, . • , xn erect ordinates xQA0 = ;y0, X\A\ = yit. x* X Fig. 1066. the vs are proportional to the corresponding slopes, and draw a smoothcurve through the points A0, Ax, A2, . . , An. This curve will aporoximate the required derivative curve. Art. 106 GRAPHICAL DIFFERENTIATION 245 Example. The following table gives the pressure p in pounds persq. in. of saturated steam at temperature 0° F. Construct the curveshowing the rate of change of pressure with respect to the temperature,dp/dd. e P Ap Ad Ap/AB 70 5 4-7 I .06 3°7-
. Graphical and mechanical computation . tangents at Bo, B\, B2, . Xi, . • , xn erect ordinates xQA0 = ;y0, X\A\ = yit. x* X Fig. 1066. the vs are proportional to the corresponding slopes, and draw a smoothcurve through the points A0, Ax, A2, . . , An. This curve will aporoximate the required derivative curve. Art. 106 GRAPHICAL DIFFERENTIATION 245 Example. The following table gives the pressure p in pounds persq. in. of saturated steam at temperature 0° F. Construct the curveshowing the rate of change of pressure with respect to the temperature,dp/dd. e P Ap Ad Ap/AB 70 5 4-7 I .06 3° 7580 5 4 4 I 14 85 5 4 2 I 19 5 4 0 I 25 323-9327 .6 90 95100 5 5 33 9 7 II 28 35 331 -1 10S 5 3 5 I 43 334-5337-8 no115 5 5 33 43 I I 4752 In the above table we have approximated dp/dd by A£/A0, , wehave replaced the (0, £) curve by a series of chords, and the slopes of thetangents by the slopes of these chords. We then plotted (0, Ap/A0) andjoined the points by a smooth curve (Fig. 106c). 120110 100 (JP)SO 8070_ t> 5-) I M > ^ V 300 310 320 ft Fig. 106c. 530 /. 34
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