  We present the SI and other unit systems, including cgs-em and cgs-es, in a
framework whereby a system of fully independent and dimensionally orthogonal
base units is modified by conventions designed to simplify the equations that
are used within each system. We propose that the radian can be seen as an
independent unit whose dimensional status is modified in the SI and other unit
systems for this purpose. This framework clarifies how different unit systems
are interrelated, and identifies the key pieces of information that are needed
to define both a unit system and the equations that are to be used with it.
Specifically, these are the size of the base units in the unsimplified system,
together with sufficient equations to identify all the conventions adopted by
the particular unit system. The appropriate extra information for the revised
SI is presented. We do not propose that the treatment of angles as
dimensionless within the SI is changed. It is also proposed that the Gaussian
unit system is best seen as identical to cgs-es, but with the B and H symbols
in equations used to represent relativistic versions of B and H, which should
properly be treated as different quantities. These different versions of B and
H can similarly be used within the SI, with many of the advantages of the
Heaviside-Lorentz system.
