Without measuring a lot of stars on many nights, folks may find that determining the second-order extinction for B or B-V reductions difficult. Unless you are observing from a very good site, the night-to-night scatter will be large. One has only to look, for instance, at Arlo Landolt’s 1992 standards paper, and Table 1 there, where he shows mean extinction and ranges in his data from Cerro Tololo, arguably one of the best places in the world to do photometry. For k’’ in B-V he shows a mean value of -0.023, but a range -0.046 to +0.013. Many observers simply adopt a reasonable value like -0.025 or -0.03 and don’t try to measure it. I would suggest PEP observers do exactly this.
In his 2019 “48 globulars” paper, Peter Stetson, arguably the most careful CCD photometrist around (he wrote DAOPhot), says “the effect is too subtle to be measured with any precision.” He adopts a fixed coefficient of -0.016 by convolving stellar energy distributions with Landolt’s B bandpass and a standard model terrestrial atmosphere for 2km altitude (i.e. typical of Arizona or Chilean sites).
Why no second-order effect in V? It is because the atmospheric extinction trend is nearly flat across the V band due to the Chappuis bands of ozone flattening the broad decline from Rayleigh extinction of ordinary gaseous air.
\Brian
the papers cited above: