. The Bell System technical journal . THE ISOGRAPH The Isograph was developed in Bell Tele-phone Laboratories to find mechanicallythe complex roots of polynomials of high degree. Let the polynomial to be factored n n n be p{z) = Sfflj-z or 2o,t^ cosjQ + iZaf^ sinjG 0 0 i if 3 = r (cos9 + isinG). The isographmaps the complex values of p{z) as thevariable describes the circle |z| = r. Thisgraph loops the origin once for each rootsmaller in absolute value than r. Thenumber of roots between trial values of ris determined by counting loops, and byinterpolation a value of r is found forwhich the gra
. The Bell System technical journal . THE ISOGRAPH The Isograph was developed in Bell Tele-phone Laboratories to find mechanicallythe complex roots of polynomials of high degree. Let the polynomial to be factored n n n be p{z) = Sfflj-z or 2o,t^ cosjQ + iZaf^ sinjG 0 0 i if 3 = r (cos9 + isinG). The isographmaps the complex values of p{z) as thevariable describes the circle |z| = r. Thisgraph loops the origin once for each rootsmaller in absolute value than r. Thenumber of roots between trial values of ris determined by counting loops, and byinterpolation a value of r is found forwhich the graph passes through the value of r and the corresponding valueof 9 define the real and imaginary parts ofa INDUSTRIAL MATHEMATICS 277 designs to be made. Generally speaking, these improvements have permitted anoverall strength increase of 20 per cent to be obtained under steady stresses,and much higher gains to be made under fatigue stress conditions; while at thesame time the certainty of obtaining the desired results on new designs has beenvery greatly enhanced. A second example was brought to my attention by Mr. L. W. Wallace,Director of the Engineering and Research Division of the Crane Company: (A) A pipe fitting weighing several hundred pounds and intended for highpressure service had a neck of elliptical cross-section. As originally designed,the thickness of the casting was intentionally not uniform, the variations havingbeen introduced empirically to strengthen it where strength was supposed to bemost needed. A redesign carried out on the basis of the theory of elasticityshowed the distribution of metal to be inefficient and resulted in a new castingin which the weight was reduced
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
