  We study the effect of confinement on solid 4-He's nonclassical rotational
inertia (NCRI) in a torsional oscillator by constraining it to narrow annular
cells of various widths. The NCRI exhibits a broad maximum value of 20% for
annuli of approximately 100 micrometer width. Samples constrained to porous
media or to larger geometries both have smaller NCRI, mostly below about 1%. In
addition, we extend Kim and Chan's blocked annulus experiment to solid samples
with large supersolid fractions. Blocking the annulus suppresses the
nonclassical decoupling from 17.1% below the limit of our detection of 0.8%.
This result demonstrates the nonlocal nature of the supersolid phenomena. At 20
mK, NCRI depends on velocity history showing a closed hysteresis loop in
different thin annular cells.
