  A self-consistent variational theory for globules based on the uniform
expansion method is presented. This method, first introduced by Edwards and
Singh to estimate the size of a self-avoiding chain, is restricted to a good
solvent regime, where two-body repulsion leads to chain swelling. We extend the
variational method to a poor solvent regime where the balance between the
two-body attractive and the three-body repulsive interactions leads to
contraction of the chain to form a globule. By employing the Ginzburg
criterion, we recover the correct scaling for the $\theta$-temperature. The
introduction of the three-body interaction term in the variational scheme
recovers the correct scaling for the two important length scales in the globule
- its overall size $R$, and the thermal blob size $\xi_{T}$. Since these two
length scales follow very different statistics - Gaussian on length scales
$\xi_{T}$, and space filling on length scale $R$ - our approach extends the
validity of the uniform expansion method to non-uniform contraction rendering
it applicable to polymeric systems with attractive interactions. We present one
such application by studying the Rayleigh instability of polyelectrolyte
globules in poor solvents. At a critical fraction of charged monomers, $f_c$,
along the chain backbone, we observe a clear indication of a first-order
transition from a globular state at small $f$, to a stretched state at large
$f$; in the intermediate regime the bistable equilibrium between these two
states shows the existence of a pearl-necklace structure.
