  We discuss the thermodynamics of an array of collinear black holes which may
be accelerating. We prove a general First Law, including variations in the
tensions of strings linking and accelerating the black holes. We analyse the
implications of the First Law in a number of instructive cases, including that
of the C-metric, and relate our findings to the previously obtained
thermodynamics of slowly accelerating black holes in anti-de Sitter spacetime.
The concept of thermodynamic length is found to be robust and a
Christoudoulou-Ruffini formula for the C-metric is shown.
