  Using a variation of the rainbow construction and various pebble and
colouring games, we prove that RRA, the class of all representable relation
algebras, cannot be axiomatised by any first-order relation algebra theory of
bounded quantifier depth. We also prove that the class At(RRA) of atom
structures of representable, atomic relation algebras cannot be defined by any
set of sentences in the language of RA atom structures that uses only a finite
number of variables.
