  We study structure and fluid-phase behaviour of a binary mixture of hard
spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states
using the $NP_nAT$ ensemble Monte Carlo (MC) method in which a normal pressure
tensor component is fixed in a system confined between two hard walls. The
method allows one to estimate the location of the isotropic-nematic phase
transition and to observe the asymmetry in the composition between the
coexisting phases, with the expected increase of the HSC concentration in the
nematic phase. This is in stark contrast with the previously reported MC
simulations where a conventional isotropic $NPT$ ensemble was used. We further
compare the simulation results with the theoretical predictions of two analytic
theories that extend the original Parsons-Lee theory using the one-fluid and
the many-fluid approximation [Malijevsk\'y {\it at al} J. Chem. Phys.
\textbf{129}, 144504 (2008)]. In the one-fluid version of the theory the
properties of the mixture are mapped on an effective one-component HS system
while in the many-fluid theory the components of the mixtures are represented
as separate effective HS particles. The comparison reveals that both the one-
and the many-fluid approaches provide a reasonably accurate quantitative
description of the mixture including the predictions of the isotropic-nematic
phase boundary and degree of orientational order of the HSC-HS mixtures.
