(6) A3-F0, III-V, $2.72 < \beta < 2.88$, $0.05 < (b-y)_0 < 0.22$, and (7) F1-G2, III-V, $2.60 < \beta < 2.72$, $0.22 < (b-y)_0 < 0.39$. The class values in this work were assigned to individual stars based on their known spectral types (provided in the XHIP catalog [@anderson2011]), and $\beta$ values where needed. In some instances, A0-A3 stars assigned to class (5) with values of $\beta < 2.87$, the dereddening procedure was unable to proceed. For these cases, stars were either assigned to class (1) if they were spectral type A0-A1, or to class (6), if they were spectral type A2-A3.

Depending on the class of an individual star, the program then calculates the dereddened indices $(b-y)_0, m_0, c_0$, the color excess $E(b-y)$, $\delta m_0$, the absolute V magnitude, $M_V$, the stellar radius and effective temperature. Notably, the $\beta$ index is unaffected by reddening as it is the flux difference between two narrow band filters with essentially the same central wavelength. Thus, no corrections are performed on $\beta$ and this index can be used robustly in coarse classification schemes.

To transform $E(b-y)$ to $A_V$, we use the extinction measurements of [@schlegel1998] and to propagate the effects of reddening 