  A theory of degenerate metrics is developed and applied to the problem of
unifying gravitation with electromagnetism. The approach is similar to the
Kaluza-Klein approach with a fifth dimension, however no ad hoc conditions are
needed to explain why the extra dimension is not directly observable under
everyday conditions. Maxwell's theory is recovered with differences only at
very small length scales, and a new formula is found for the Coulomb potential
that is regular everywhere.
