  We extend the operations of shorting and parallel addition from the cone of
bounded nonnegative selfadjoint operators in a Hilbert space to the set of all
nonnegative selfadjoint linear relations. New properties of these operations
and connections with the Cayley transforms are established. It is shown that
for a pair of nonnegative selfadjoint linear relations there exist, in general,
two arithmetic--harmonic means. Applications of the arithmetic, harmonic, and
arithmetic--harmonic means to the theory of nonnegative selfadjoint extensions
of nonnegative symmetric linear relations are given.
