  Dust extinction is one of the fundamental measurements of dust grain sizes,
compositions, and shapes. Most of the wavelength dependent variations seen in
Milky Way extinction are strongly correlated with the single parameter
R(V)=A(V)/E(B-V). Existing R(V) dependent extinction relationships use a
mixture of spectroscopic and photometry observations, hence do not fully
capture all the important dust features nor continuum variations. Using four
existing samples of spectroscopically measured dust extinction curves, we
consistently measure the R(V) dependent extinction relationship
spectroscopically from the far-ultraviolet to mid-infrared for the first time.
Linear fits of A(lambda)/A(V) dependent on R(V) are done using a method that
fully accounts for their significant and correlated uncertainties. These linear
parameters are fit with analytic wavelength dependent functions to determine
the smooth R(V) (2.3-5.6) and wavelength (912 A-32 micron) dependent extinction
relationship. This relationship shows that the far-UV rise, 2175 A bump, and
the three broad optical features are dependent on R(V), but the 10 and 20
micron features are not. Existing literature relationships show significant
deviations compared to this relationship especially in the far-ultraviolet and
infrared. Extinction curves that clearly deviate from this relationship
illustrate that this relationship only describes the average behavior versus
R(V). We find tentative evidence that the relationship may not be linear with
1/R(V) especially in the ultraviolet. For the first time, this relationship
provides measurements of dust extinction that spectroscopically resolve the
continuum and features in the ultraviolet, optical, and infrared as a function
of R(V) enabling detailed studies of dust grains properties and full
spectroscopic accounting for the effects of dust extinction on astrophysical
objects.
