  There are large uncertainties in the predictions of the boron neutrino flux
from the Sun which cannot be considered as being of purely statistical origin.
We treat the magnitude of this flux, $\Phi_B$, as a parameter to be found from
experiment. The properties of the MSW solution to the solar neutrino problem
for different values of $\Phi_B$ are studied. Present data give the bounds:
$0.38 < \Phi_B/ \Phi_B^0 < 3.1$ (2$\sigma$), where $\Phi_B^0 \equiv 5.7 \cdot
10^6$ cm$^{-2}$s$^{-1}$ is the flux in the reference SSM. The variations of the
flux in this interval enlarge the allowed region of mixing angles: $\sin^2
2\theta = 8\cdot 10^{-4} \div 2\cdot 10^{-2}$ (small mixing solutions) and
$\sin^2 2\theta = 0.2 \div 0.85$ (large mixing solution). If the value of the
original boron neutrino flux is about that measured by Kamiokande, a consistent
description of the data is achieved for $\sin^2 2\theta \sim (0.8 \div 2)\cdot
10^{-3}$ (``very small mixing solution"). The solution is characterized by a
strong suppression of the beryllium neutrino line, a weak distortion of the
high energy part of the boron neutrino spectrum and a value of the double ratio
$(CC/NC)^{exp}/(CC/NC)^{SSM}$ at $E > 5$ MeV close to 1. We comment on the
possibility to measure the neutrino parameters and the original boron neutrino
flux in future experiments.
