  Cremona, Mazur, and others have studied what they call visibility of elements
of Shafarevich-Tate groups of elliptic curves. The analogue for an abelian
number field $K$ is capitulation of ideal classes of $K$ in the minimal
cyclotomic field containing $K$. We develop a new method to study capitulation
and use it and classical methods to compute data with the hope of gaining
insight into the elliptic curve case. For example, the numerical data for
number fields suggests that visibility of nontrivial Shafarevich-Tate elements
might be much more common for elliptic curves of positive rank than for curves
of rank 0.
