  In the $(\epsilon_1-\epsilon_2)^2$--approximation the Casimir energy of a
dilute dielectric ball is derived using a simple and clear method of the mode
summation. The addition theorem for the Bessel functions enables one to present
in a closed form the sum over the angular momentum before the integration over
the imaginary frequencies. The linear in $(\epsilon_1-\epsilon_2)$ contribution
into the vacuum energy is removed by an appropriate subtraction. The role of
the contact terms used in other approaches to this problem is elucidated.
