  We clarify the status of the $c$ equivalence principle ($c_u=c$) recently
proposed by Heras et al \cite{JoseAJP2010,JoseEJP2010} and show that its
proposal leads to an extension of the current framework of classical
relativistic electrodynamics (CRE). This is because in the MLT (mass, length
and time) system of units, CRE theory can contain only one fundamental constant
of nature and special relativity dictates that this must be $c$, the standard
speed of light in vacuum, a point not sufficiently emphasized in most textbooks
with the exception of a few such as Panofsky and Phillips
\cite{PanofskyPhillips}. The $c$ equivalence principle Heras
\cite{JoseAJP2010,JoseEJP2010} can be shown to be linked to the second
postulate of special relativity which extends the constancy of the unique
velocity of light to all of physics (especially to mechanics) other than
electromagnetism. An interesting corollary is that both the weak equivalence
principle of general relativity and the $c$ equivalence principle are in fact
one and the same, which we demonstrate within the context of Newtonian gravity.
