  In this paper we construct certain higher Chow cycles in the $K_{1}$ of the
Jacobian of Fermat curves, generalising a construction of Collino. We further
compute the regulator of these elements in terms of special values of
hypergeometric functions. Otsubo has computed the regulator of certain elements
of $K_0$ and $K_2$ of Fermat varieties and this paper is along the same lines.
