  We study Dedekind sums $S(a,b)$ near Farey points of the interval $[0,b]$.
Each of these Dedekind sums is connected with a set of other Dedekind sums by
the Petersson-Knopp identity. In the case considered here, this identity has a
very specific interpretation, inasmuch as each Dedekind occurring in this
identity is close to a certain expected value. Conversely, each of these
expected values occurs with a certain frequency, a frequency that is consistent
with the Petersson-Knopp identity.
