  The wave function of a spheroidal harmonic oscillator without spin-orbit
interaction is expressed in terms of associated Laguerre and Hermite
polynomials. The pairing gap and Fermi energy are found by solving the BCS
system of two equations. Analytical relationships for the matrix elements of
inertia are obtained function of the main quantum numbers and potential
derivative. They may be used to test complex computer codes one should develop
in a realistic approach of the fission dynamics. The results given for the
$^{240}$Pu nucleus are compared with a hydrodynamical model. The importance of
taking into account the correction term due to the variation of the occupation
number is stressed.
