  In this note, we compare two different definitions for the cosmological
perturbation $\zeta$ which is conserved on large scales, and study their
non-conservation on small scales. We derive an equation for the time evolution
of the curvature perturbation on a uniform density slice through a calculation
solely in longitudinal (conformal-Newtonian) gauge. The result is concise and
compatible with that obtained via local conservation of energy-momentum tensor.
