  The effect of surface anisotropy on the distribution of energy barriers in
magnetic fine particles of nanometer size is discussed within the framework of
the $T\ln(t/\tau_0)$ scaling approach. The comparison between the distributions
of the anisotropy energy of the particle cores, calculated by multiplying the
volume distribution by the core anisotropy, and of the total anisotropy energy,
deduced by deriving the master curve of the magnetic relaxation with respect to
the scaling variable $T\ln(t/\tau_0)$, enables the determination of the surface
anisotropy as a function of the particle size. We show that the contribution of
the particle surface to the total anisotropy energy can be well described by a
size--independent value of the surface energy per unit area which permits the
superimposition of the distributions corresponding to the particle core and
effective anisotropy energies. The method is applied to a ferrofluid composed
of non-interacting Fe$_{3-x}$O$_{4}$ particles of 4.9 nm in average size and
$x$ about 0.07. Even though the size distribution is quite narrow in this
system, a relatively small value of the effective surface anisotropy constant
$K_{s}=2.9\times 10^{-2}$ erg cm$^{-2}$ gives rise to a dramatic broadening of
the total energy distribution. The reliability of the average value of the
effective anisotropy constant, deduced from magnetic relaxation data, is
verified by comparing it to that obtained from the analysis of the shift of the
ac susceptibility peaks as a function of the frequency.
