. Graphical and mechanical computation . O II ^ ItcJ %^ li ii II ii it Jl* ?j a i O Art. iio MECHANICAL DIFFERENTIATION 255 iio. Mechanical differentiation. Themachine which draws the derivative curve y Differentiator. — Thisdy is a dx of the curve y = f(x). Since the ordinate of the derivative curve is equal to the slope of the in-tegral curve, it is necessary to construct the tangent lines at a series ofpoints of the integral curve. We have already mentioned (Art. 106) theuse of a strip of celluloid with two black dots on its under side to deter-. Fig. no. mine the direction of the tangent.
. Graphical and mechanical computation . O II ^ ItcJ %^ li ii II ii it Jl* ?j a i O Art. iio MECHANICAL DIFFERENTIATION 255 iio. Mechanical differentiation. Themachine which draws the derivative curve y Differentiator. — Thisdy is a dx of the curve y = f(x). Since the ordinate of the derivative curve is equal to the slope of the in-tegral curve, it is necessary to construct the tangent lines at a series ofpoints of the integral curve. We have already mentioned (Art. 106) theuse of a strip of celluloid with two black dots on its under side to deter-. Fig. no. mine the direction of the tangent. This scheme is used in a differentiatingmachine constructed by J. E. Murray.* In a differentiating machinerecently constructed by A. a silver mirror is used for de-termining the tangent. The mirror is placed across the curve so thatthe curve and its image form a continuous unbroken line, for then thesurface of the mirror will be exactly normal to the curve, and a perpen-dicular to this at the point of intersection of the mirror and the curve willgive the direction of the tangent line. If the surface of the mirror de- * Proc. Roy. Soc. of Edinburgh, May, 1904. f Scientific American Supplement, Feb. 12, 1916. 256 APPROXIMATE INTEGRATION AND DIFFERENTIATION Chap. IX viates even slightly from the normal, a break will occur at the point wherethe image and curve join. It is claimed that with a little practice a re-markable degree of accuracy can be obtained in setting the mirror. Fig. no gives a diagram illustrating the working of this
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