If a railway circular curve spring directly from the tangent, the curvature at the point of contact is discontinuous, since it is zero for the straight line, and finite for the circle. This causes shock whenever rolling stock enters the curve, and at high speeds this is a matter of danger. Further, the outer rail is elevated on the curve, while the rails are at the same level on the straight. This indicates a further discontinuity. The transition curve is introduced to give both a gradual change of curvature and a gradual cant or super-elevation of the outer rail.