optical, our fit to SDSS spectrum &$22\,410 \pm 175$& $8.12 \pm 0.02$\
HST, this paper &$20\,565 \pm 82$ & $8.19 \pm 0.03$\
adopted, this paper (Sect. \[s-teff\_logg\]) &$20900 \pm 900$& $8.15 \pm 0.04$\
\
optical, [@vennesetal10-1] & $20\,890 \pm 120$& $7.90 \pm 0.03$\
optical, [@melisetal11-1] & $23\,470 \pm 300$& $7.99 \pm 0.05$\
HST, this paper & $21\,200 \pm 50$ & $7.91 \pm 0.02$\

![image](PG0843+516_cosfit.eps){width="\columnwidth"} ![image](PG1015+161_cosfit.eps){width="\columnwidth"}

![image](SDSS1228+1040_cosfit.eps){width="\columnwidth"} ![image](GALEX1931+0117_cosfit.eps){width="\columnwidth"}

Atmosphere models
=================

\[s-teff\_logg\]Effective temperature and surface gravity
---------------------------------------------------------

All observed *HST*/COS and optical spectra were analysed with theoretical model atmospheres using input physics as described in @koester10-1, and including the Lyman and Balmer line profiles of @tremblay+bergeron09-1. We used a fine grid of models spanning the range of temperatures and surface gravities found for the four targets by previous studies (Table \[t-parameters\]) and determined the best-fit parameter by minimising $\chi^2$, using the very good relative flux calibration as an additional constraint. The errors reported in Sect.\[s-notes\] are statistical only and do not include systematic effects of observation, reduction, or models. More realistic errors can be estimated from a comparison with the other measurements in the literature, which used similar models, but optical spectra. Table \[t-parameters\] suggests a systematic trend for somewhat lower 