  The central (surface) energy-density, $E_0 (E_R)$, which appears in the
expression of total static and spherical mass, $M$ (corresponding to the total
radius $R$) is defined as the density measured only by one observer located at
the centre (surface) in the Momentarily Co-moving Reference Frame (MCRF). Since
the mass, $M$, depends only on the central (surface) density for most of the
equations of state (EOSs) and/or exact analytic solutions of Einstein's field
equations available in the literature, the central (surface) density measured
in the preferred frame (that is, in the MCRF) appears to be not in agreement
with the coordinate invariant form of the field equations that result for the
source mass, $M$. In order to overcome the use of any preferred coordinate
system (the MCRF) defined for the central (surface) density in the literature,
we argue for the first time that the said density may be defined in the
coordinate invariant form, that is, in the form of the average density
($3M/4\pi R^3)$ of the the configuration which turns out to be independent of
the radial coordinate $`r'$ and depends only on the central (surface) density
of the configuration. In this connection, we further argue that the central
(surface) density of the structure should be {\em independent} of the density
measured on the other boundary (surface/central) because there exists no a
priori relation between the radial coordinate $`r'$ and the proper distance
from the centre of the sphere to its surface \cite{Ref1}. In the light of this
reasoning, the various EOSs and analytic solutions of Einstein's field
equations in which the central and the surface density are {\em interdependent}
can not fulfill the definition of central (surface) density measured only by
one observer located in the MCRF at the centre (surface) of the configuration.
