We have measured the critical Velocity upsilon(c) at which He-3-A in a
rotating cylinder becomes unstable against the formation of quantized
vortex lines with continuous (similarity-free) core structure. We fin
d that upsilon(c) is distributed between a maximum and a minimum limit
, which we ascribe to a dependence on the texture or the orbital angul
ar momentun axis (I) over cap(r) in the cylinder. Slow cooldown throug
h T-c in rotation yields (I) over cap(r) textures for which the measur
ed upsilon(c)'s are in good agreement with the calculated instability
of the expected (I) over cap texture.