Let f be analytic and univalent in Δ={z:[mid ]z[mid ]<1}. We write

formula here

for 0[les ]r<1 and θ∈[0, 2π], and remark that L(r, θ) is the length of the image in f(Δ) of the ray joining 0 to reiθ in Δ. We shall be concerned with the growth of L(r, θ), as a function of r, for univalent functions in Δ and, more particularly, for functions in the subclass of close-to-convex univalent functions in Δ.