The temperature, T, dependence of the magnetic penetration depth, lambda, o
f grain-aligned YBa2Cu4O8 has been measured along the ab plane and c axis.
Both lambda(ab)(T) and lambda(c)(T) vary as root T up to similar to 0.4T(c)
implying a square-root density of states at low energy. The results are di
scussed in terms of a proximity model of alternating stacked superconductin
g and normal layers. [S0163-1829(99)51310-6].