  We present the theory of liquid bridges between two axisymmetric solids,
sphere and plane, with prescribed contact angles in a general setup, when the
solids are non-touching, touching or intersecting, We give a detailed
derivation of expressions for curvature, volume and surface area of pendular
ring as functions of the filling angle \psi for all available types of menisci:
catenoid Cat, sphere Sph, cylinder Cyl, nodoid Nod and unduloid Und (the
meridional profile of the latter may have inflection points).
  The Young-Laplace equation with boundary conditions can be viewed as a
nonlinear eigenvalue problem. Its unduloid solutions, menisci shapes z_n^s(r)
and their curvatures H_n^s(\psi), exhibit a discrete spectrum and are
enumerated by two indices: the number n of inflection points on the meniscus
meridional profile M and the convexity index s=\pm 1 determined by the shape of
a segment of M contacting the solid sphere: the shape is either convex, s=1, or
concave, s=-1.
  For the fixed contact angles the set of the functions H_n^s(\psi) behaves in
such a way that in the plane (\psi,H) there exists a bounded domain where
H_n^s(\psi) do not exist for any distance between solids. The curves
H_n^s(\psi) may be tangent to the boundary of domain which is a smooth closed
curve. This topological representation allows to classify possible curves and
introduce a saddle point notion. We observe several types of saddle points, and
give their classification.
