Excerpt from The Transition Curve, or Curve of Adjustment as Applied to the Alignment of Railroads: By the Method of Rectangular Co-Ordinates and by Deflection Angles (or Polar Co-Ordinates)

That of joining a tangent with a circular curve, by means of the transition curve, is a special case where one of the radii becomes infinitely great. Some of the recent spirals, adopted as curves of adjustment in railroad location, easily develop from the equations of the cubic parabola by making the proper substitutions in them.

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