We discuss the definitions of standard clocks in theories of gravitati
on. These definitions are motivated by the invariance of actions under
different gauge symmetries. We contrast the definition of a standard
Weyl clock with that of a clock in general relativity and argue that t
he historical criticisms of theories based on non-metric compatible co
nnections by Einstein, Pauli and others must be considered in the cont
ext of Weyl's original gauge symmetry. We argue that standard Einstein
ian clocks can be defined in non-Riemannian theories of gravitation by
adopting the Weyl group as a local gauge symmetry that preserves the
metric and discuss the hypothesis that atomic clocks may be adopted to
measure proper time in the presence of non-Riemannian gravitational f
ields. These ideas are illustrated in terms of a recently developed mo
del of gravitation based on a non-Riemannian spacetime geometry.