. Graphical and mechanical computation . dinates dividedby the length of the base is the m. s. c. p. of the lamp, and this valuemultiplied by 4 t will give the flux in lumens. To measure the required area we have constructed the integral curve(Fig. 105/z) by the method described above. We chose 7 in. for thelength of the diameter of the circle and 1 in. = 10 c-p in laying off the ordi-nates. The y-axis or axis to which the horizontals are extended is drawn5 in. to the right of the point A0, so that the polar distance is A0O = a= 5 in. The area under the curve A0AiA2 . . A12 is measured by the
. Graphical and mechanical computation . dinates dividedby the length of the base is the m. s. c. p. of the lamp, and this valuemultiplied by 4 t will give the flux in lumens. To measure the required area we have constructed the integral curve(Fig. 105/z) by the method described above. We chose 7 in. for thelength of the diameter of the circle and 1 in. = 10 c-p in laying off the ordi-nates. The y-axis or axis to which the horizontals are extended is drawn5 in. to the right of the point A0, so that the polar distance is A0O = a= 5 in. The area under the curve A0AiA2 . . A12 is measured by the ordi-nate #i2-Bi2 = Since y = — X area, therefore area = a X y = 5X = sq. in. Since 1 in. on the scale of ordinates represents 25 1 x TO 10 c-p and the base of the diagram is 7 in., the m. s. c. p. = -^ = 33-3 C~P- The straight line A0Bu will cut the y-axis in a point D suchthat OD read on the c-p scale will also give the m. s. c. p., for Am. 105 GRAPHICAL INTEGRATION AoO A0x12 base base We measure OD = c-p. 243. Fig. 105/1. E. L. Clark Having drawn the integral curve we may immediately find them. s. c. p. of any portion of the lamp between two sections. Thus, for 150 244 APPROXIMATE INTEGRATION AND DIFFERENTIATION Chap. IX on each side of the vertical, the m. s. c. p. is found by drawing A0E parallelto Bf>B7 and reading OE = c-p on the candle-power scale, since OEa x-,Bi — XsB-o or OE = area under A5A7base = m. s. c. p. Similarly the m. s. c. p. of the section above a horizontal planethrough the lamp is measured by OF = c-p, and the m. s. c. p. ofthe section below a horizontal plane through the lamp is measured byOG = c-p. 106. Graphical differentiation. — If the integral curve y = f(x) is given we may construct the derivative curve y = ~~ by using the prin- ax ciple that the ordinate of the derivative curveat any point P (x, y) (Fig. 106a) is equal tothe slope of the integral curve or of thetangent line PT at the corresponding poin
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