  The globular clusters (GC) of our Galaxy have been found to lie close to a
plane in the log(R_e), log(sigma), SB_e space, on the continuation of the
Fundamental Plane (FP) known to characterize the properties of early-type
galaxies. We reexamine the issue on a sample of 48 GCs selected in terms of
homogeneity criteria for the photometric data available from the literature and
perform a model-independent analysis of surface brightness profiles (SBP) and
distance moduli, estimating error bars and studying selection effects with
non-parametric statistical tests. We determine the coefficients of the FP and
their error bars. The scatter from the FP relation is likely to be intrinsic,
i.e. not due to measurement errors only. We find that in the standard FP
coordinates our sample occupies a slim, axisymmetric region of parameter space,
suggesting that the scaling relation might be around a Fundamental Line, rather
than a plane, confirming a result noted earlier. This is likely to be the
origin of the difficulties in the fit by a plane mentioned in previous
investigations. Such FL relation would imply a pure photometric scaling law,
which might be tested on wider samples and on extra-galactic GC systems. We
find a correlation of the residuals from the FP relation with the central slope
of the SBP. No other correlations are found. Finally, we reconstruct the
distribution of the values of the quantity log(K_V/(M/L)) (virial coefficient
divided by the mass-to-light ratio) through kernel density estimation and find
evidence for bimodality, which suggests that the galactic GC system may be
composed of at least two dynamically different populations. Yet, these
populations do not reflect the standard dichotomy between disk and halo
clusters. (abridged).
