For a strong, stationary double layer to be maintained, the electron f
lux PHI(e) and the ion flux PHI(i) must satisfy the Langmuir condition
PHI(e)/PHI(i) = square-root m(i)/m(e). However, this condition alone
does not determine whether or not the double layer will remain in stab
le equilibrium at a given position. A new stability condition is obtai
ned and the results of several laboratory double layer experiments are
examined using this condition.