  We present an L-A pair for the Apel'rot case of a heavy rigid 3-dimensional
body. Using it we give an algebro-geometric integration procedure. Generalizing
this L-A pair, we obtain a new completely integrable case of the Euler-Poisson
equations in dimension four. Explicit formulae for integrals which are in
involution are given. This system is a counterexample to one well known Ratiu's
theorem. Corrected version of this classification theorem is proved.
