  We compute the degree of Hurwitz-Hodge classes $\lambda_1^e$ on one
dimensional moduli spaces of cyclic admissible covers of the projective line.
We also compute the degree of the the first Chern class of the Hodge bundle
$\lambda_1$ for all one dimensional moduli spaces. In higher dimension, we
express the divisor class $\lambda_1$ as a linear combination of $\psi$ classes
and boundary strata.
