The fourth-order virial expansion represents an important tool in the descr
iption of the equilibrium behaviour of pure fluids and mixtures in the vici
nity of their critical point/critical region. Dependences of cluster integr
als D-4(HCB), D-5(HCB) and D-6(HCB) of hard convex bodies on the geometric
characteristics (i.e. the volume, surface area and the mean curvature integ
ral of the given body) form the basic information necessary for the evaluat
ion of the fourth virial coefficient, D, of Kihara non-spherical molecules.
We determined D-4(HCB), D-5(HCB) and D-6(HCB) for pure prolate and oblate
hard spherocylinders with the non-sphericity parameter alpha is an element
of (1, 3). A Monte Carlo integration technique was employed and the individ
ual contributions D-4(HCB)/V-3, D-5(HCB)/V-3 and D-6(HCB)/V-3 were expresse
d as quadratic functions of alpha, with coefficients (integral quantities)
obtained by a three-step fitting procedure. Values of the HCB fourth virial
coefficient (obtained as an algebraic sum of m(i)D(i)(HCB)) for the indivi
dual types of molecules agree well with the pseudo-experimental data from t
he literature. The expressions for D-i(PS) and D-i(OS) as well as that for
the total fourth virial coefficient for prolate and oblate spherocylinders
differ considerably; none of the one-parameter equations of state (proposed
for HCB systems) yields an expression predicting correctly the fourth viri
al coefficient of HCBs in the considered range of alpha. An attempt is made
to express the fourth virial coefficient in terms of two non-sphericity pa
rameters; different results for prolate and oblate hard spherocylinders wer
e obtained.