The late infall of dark matter onto a galaxy produces structure (such as ca
ustics) in the distribution of dark matter in the halo. We argue that such
structure is likely to occur generically on length scales proportional to l
similar to t(0)v(rot), where ro is the age of the universe and v(rot) is t
he rotation velocity of the galaxy. A set of 32 extended galactic rotation
curves is analyzed. For each curve, the radial coordinate is rescaled accor
ding to r-->(r) over tilde = r(v(0)/v(rot)), where we choose v(0) = 220 km/
s. A linear fit to each rescaled rotation curve is subtracted, and the resi
duals are binned and averaged. The sample shows significant features near (
r) over tilde = 40 kpc and (r) over tilde = 20 kpc. This is consistent with
the predictions of the self-similar caustic ring model of galactic halos.