. Railway and locomotive engineering : a practical journal of railway motive power and rolling stock . Vereins deutsches Ingenieurs, 1907, butas it gives results that are inaccurate, orit may be better to say incorrect, it ispassed by here. A second solution hasalso been put out by these same workswhich is a method of calculation and waspublished in 1905 of the Zeitschrift dcsVereins deutsches Ingenieurs. Althoughit may be used in practice it is not recom- 118 RAILWAY AND LOCOMOTIVE ENGINEERING May, 1922 mended because of the greater amount oftime that will be consumed in making sucha mathemat
. Railway and locomotive engineering : a practical journal of railway motive power and rolling stock . Vereins deutsches Ingenieurs, 1907, butas it gives results that are inaccurate, orit may be better to say incorrect, it ispassed by here. A second solution hasalso been put out by these same workswhich is a method of calculation and waspublished in 1905 of the Zeitschrift dcsVereins deutsches Ingenieurs. Althoughit may be used in practice it is not recom- 118 RAILWAY AND LOCOMOTIVE ENGINEERING May, 1922 mended because of the greater amount oftime that will be consumed in making sucha mathematical calculation, whereas theresults can be obtained, in one half thetime, in all of their completeness, by themethod of trial that is suggested. Suppose, then, that tlie point D is solocated that it fulfills the requirement of 2. Take X; (on the left side of the equa-tion) very slightly more than x^ (on theright hand side of the equation). Thus the exact value of x can be mostquickly determined by the graphicalmethod. Draw Fig. 15 on the largest scale pos-sible, and in a system of rectangular co-. DDt = DD,, it then becomes possible todeduce the following equations from : Chord DD^ = Chord DD,Hence a -|- 6° == c + dBecause a, b, c and d are the two sidesrespectively of the triangles D, D H andD K D-, of which the two equal chords arethe hypothenuses. .Also from the triangleD A E we have x 4- f^ = R=and from the triangle D, CE (X + b)= -f (f — a)^= Rand from DjFE(;r - cY- 4- (/ + dr = Rfrom B O D r + U — x) = Ifrom D, HB, o=-f (g + r —;r — &) = ffrom D,KB, df-ir{g — r — x+cy = PBecause of the equalization of the arcsDDi and DD. we also have an equaliza-tion of the distances K L = dbecause the angles D M A and D M Dxare equal, and from the similarity of thetriangles Di H M and K L M. we alsohave a : 2x -\- h — d : 2x — eliminating the unknown quanti-ties a, b, c, d, I, and R from these equa-tions, we obtain an equation of the thirddegree for the v
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