  This paper is concerned with the Laplace boundary-value problem with the
directional derivative, corresponding to the specific nature of measurements of
the longitudinal component of the photospheric magnetic field. Boundary
conditions are specified by a distribution on the sphere of projection of the
magnetic field vector unto a given direction. It is shown that the solution of
this problem exists in the form of a spherical harmonic expansion, and
uniqueness of this solution is proved. A conceptual sketch of numerical
determination of the harmonic series coefficients is given. The field of
application of the method is analyzed having regard to the peculiarities of
actual data. Finally, we present differences in results derived from
extrapolating the magnetic field from a synoptic map and a full-disk
magnetogram.
