In this paper we describe a new approach for measuring the mean longitudina
l magnetic field and net linear polarization of Ap and Bp stars. As was dem
onstrated by Wade et al., least-squares deconvolution (LSD; Donati et al.)
provides a powerful technique for detecting weak Stokes V, Q and U Zeeman s
ignatures in stellar spectral lines. These signatures have the potential to
apply strong new constraints to models of stellar magnetic field structure
. Here we point out two important uses of LSD Stokes profiles. First, they
can provide very precise determinations of the mean longitudinal magnetic f
ield. In particular, this method allows one frequently to obtain 1 sigma er
ror bars better than 50 G, and smaller than 20 G in some cases. This method
is applicable to both broad- and sharp-lined stars, with both weak and str
ong magnetic fields, and effectively redefines the quality standard of long
itudinal field determinations. Secondly, LSD profiles can in some cases pro
vide a measure of the net linear polarization, a quantity analogous to the
broad-band linear polarization recently used to derive detailed magnetic fi
eld models for a few stars (e.g. Leroy et al.). In this paper we report new
high-precision measurements of the longitudinal fields of 14 magnetic Ap/B
p stars, as well as net linear polarization measurements for four of these
stars, derived from LSD profiles.