  Let {\alpha}(s) be an arc on a connected oriented surface S in E3,
parameterized by arc length s, with torsion {\tau} and length l. The total
square torsion F of {\alpha} is defined by T=\int_{0}^{l}\tau ^{2}ds\ $. . The
arc {\alpha} is called a relaxed elastic line of second kind if it is an
extremal for the variational problem of minimizing the value of F within the
family of all arcs of length l on S having the same initial point and initial
direction as {\alpha}. In this study, we obtain differential equation and
boundary conditions for a relaxed elastic line of second kind on an oriented
surface.
