We present a detailed spectroscopic analysis of the H and He I spectru
m of the Luminous Blue Variable (LBV) P Cygni. The observational const
raints for our investigation are given by the mean optical and near-IR
spectra obtained by Stahl et al. (1993) and published UV, optical, IR
and radio continuum measurements of the star. Within the parameter do
main of interest we have investigated how line strengths, line shapes
and the emergent energy distribution behave as a function of stellar p
arameters such as temperature, luminosity, wind density, etc. The sens
itivity of the H and He I line profiles to model parameters allows a q
uantitative spectroscopic analysis of P Cygni to be performed. The der
ived parameters for P Cygni place it near a regime where two classes o
f models exist - those in which H remains fully ionized in the wind, a
nd those in which H eventually recombines in the wind. The transition
between the two classes of models is dramatic - a 5% change in luminos
ity or mass-loss is sufficient. The shape of the P Cygni absorption on
the H alpha profile and the radio variability indicates that H must r
ecombine in P Cygni's wind. As for Wolf-Rayet (W-R) stars we find that
we can generate a set of homologous models which are capable of expla
ining, within observational errors, the flux distribution and the line
profiles equally well. Scaling relations for the homologous models ha
ve been determined, but to first order they have the same T-eff and th
e same wind density parameter ((M) over dot/R(1.5)). Consequently it
is impossible to derive R from a spectroscopic analysis. Assuming R*=
75 R., the following stellar parameters for P Cygni are derived: [GRAP
HICS] These imply a stellar distance of 1.7 +/- 0.1 kpc, which is cons
istent with determinations in the literature. Continuum fluxes and the
observed optical and near-infrared H and He I line profiles are well
reproduced by the model. The derived stellar parameters and the high h
elium abundance indicates that P Cygni is highly evolved.