  A classification of Brans-Dicke theories of gravitation, based on the
behaviour of the dimensionless gravitational coupling constant, is given. It is
noted that the discussion takes place in the current literature, about which of
the two distinguished conformal frames in which scalar-tensor theories of
gravity can be formulated: the Jordan frame and the Einstein frame, is the
physical one, may, in most cases, be meaningless for both frames may belong to
the same conformal class. It is also noted that the Jordan frame formulation of
Brans-Dicke gravity with ordinary matter nonminimally coupled, that is shown to
be just the Jordan frame formulation of general relativity, is scale-invariant,
unlike the situation with the Jordan frame representation of Brans-Dicke
gravity with matter minimally coupled (the original formulation of Brans-Dicke
theory), where the presence of nonzero mass ordinary matter breaks the
scale-invariance of the theory.
