Trying to understand the constant factors (19 and 38) in Ed25519 ref10 function 'fe_mul'
The section 'Radix-$2^{64}$ representation' on page 11 of the Ed25519 paper ("High-speed high-security signatures" by Bernstein et al.) actually explains the technique. I should have read the paper more carefully.

As pointed out by CodesInChaos, the order of the field is $p=2^{255}-19$ and the 38 corresponds to $2p=2^{256}-38$.