  This work deals with the study of an erupting prominence embedded in the core
of a CME and focuses on the derivation of the prominence plasma filling factor.
We explore two methods to measure the prominence plasma filling factor that are
based on the combination of visible-light and ultraviolet spectroscopic
observations. Theoretical relationships for resonant scattering and collisional
excitation are used to evaluate the intensity of the H I Lyman-{\alpha} and
Lyman-{\beta} lines, in two prominence points where simultaneous and cospatial
LASCO-C2 and UVCS data were available. Thermodynamic and geometrical parameters
assumed for the calculation are provided by both observations and the results
of a detailed 1D non-LTE radiative-transfer model of the prominence, developed
in our previous work (Heinzel 2016). The filling factor is derived from the
comparison between the calculated and the measured intensities of the two
lines. The results are then checked against the non-LTE model in order to
verify the reliability of the methods. The resulting filling factors are
consistent with the model in both the prominence points when the separation of
the radiative and collisional components of the total intensity, required to
estimate the filling factor, is performed using both the line intensities. An
exploration of the parameter space shows that the results are weakly sensitive
to the plasma velocity, but they depends more strongly on the assumed kinetic
temperatures. The combination of visible-light and ultraviolet Lyman-{\alpha}
and Lyman-{\beta} data can be used to approximately estimate the geometrical
filling factor in erupting prominences, but the proposed techniques are
reliable only for emission that is optically thin in the lines considered,
condition that is not in general representative of prominence plasma.
