Since the discovery, almost 50 years ago, of a magnetic field in the
Ap star 78 Vir (Babcock 1947), until recently, the vast
majority of the investigations of Ap star magnetic fields have been devoted
to the determination of their mean longitudinal magnetic field (see
e.g. the reviews of Mathys 1989 and Landstreet
1992). The latter, to which one often refers more briefly as the
longitudinal field
, is the line-intensity weighted average over the visible
stellar hemisphere of the line-of-sight component of the magnetic vector.
It is diagnosed from the observation of circular polarization in spectral
lines. From studies of this field moment, and in particular of its
variation with stellar rotation, a general picture of the
magnetic fields of Ap stars could be obtained. As a result, it is now
well established that those fields have a large-scale organization,
which in most cases bears some resemblance to
a dipole whose axis is inclined with
respect to the stellar rotation axis. The brightness and abundance
inhomogeneities of the stellar surface appear grossly related to the
field geometry. Thus the study of the latter should prove essential for
the understanding of the origin of the former, and more generally of
the physical processes at work in the atmospheres not only of the Ap
stars, but also probably of many upper main-sequence stars. However, the
derivation of the magnetic field geometry cannot be achieved from the
consideration of the mean longitudinal field alone.
One subgroup of the Ap stars lend themselves particularly well to more detailed studies of their magnetic fields: these are the stars whose spectral lines, when observed (in unpolarized light) at sufficiently high dispersion, are resolved into several magnetically split components. In these stars, one can determine in a straightforward, mostly approximation-free, model-independent manner, and with particularly great precision, the mean magnetic field modulus, or in short the (mean) field modulus. This quantity, which in previous works was often called the surface field, is the line-intensity weighted average over the visible stellar hemisphere of the modulus of the magnetic vector.
It had been realized 25 years ago already that by combining the knowledge of the variations of the field modulus and of the longitudinal field throughout the stellar rotation cycle, one could derive much better constraints on the field structure than from the consideration of the longitudinal field alone. By 1972, this approach had been applied successfully to 4 stars: HD 65339 (Huchra 1972), HD 126515 (Preston 1970), HD 137909 (Wolff &\ Wolff 1970), and HD 215441 (Preston 1969a). Preston (1971a) had discovered 5 more stars with magnetically resolved lines (HD 12288, HD 81009, HD 165474, HD 188041, and HDE 335238). But no attempts had been made to measure their mean field modulus throughout their rotation cycle until we started the project reported here.
Renewed interest in the modeling of the geometric structure of Ap star magnetic fields has arisen in the last few years, thanks to the technological progress made both in astronomical instrumentation (in particular, detectors) and in computers. Accordingly, it has become possible to collect astronomical data of unprecedented accuracies (making possible e.g. fine studies of the profiles of polarized spectral lines), which can be modeled more realistically than ever before. For instance, Landstreet and his collaborators have carried out refined studies of the magnetic field geometry of HD 65339 (Landstreet 1988) and of HD 215441 (Landstreet et al. 1989), by simultaneously modeling their unpolarized spectral line profiles and the variations of their longitudinal field. Mathys (1995a, b) has analyzed the circularly polarized line profiles of a sample of Ap stars observed throughout their rotation cycle using the moment technique that he has developed (Mathys 1988). Leroy et al. (1995) have derived models of the fields of the stars HD 62140, HD 71866, and HD 137909, from their observations of broadband linear polarization along the rotation periods of these stars. These are but a few examples of the recently published works in the field.
Still, the very favourable circumstances presented by the stars with resolved magnetically split lines for the diagnosis of the field geometry are far from having been fully exploited. By the end of the 1980's, only 4 of the 9 stars of this kind known in the early 1970's had been studied in detail. A few additional such stars had been discovered in isolated studies: HD 200311 (Preston, cited by Adelman 1974), HD 201601 (a somewhat marginal detection reported by Scholz 1979), and HD 187474 (Didelon 1987). But there had been no systematic study of these stars, nor attempt to find more of them. Therefore, it seemed appropriate to undertake a large-scale project of extensive investigation of the Ap stars with resolved magnetically split lines.
This programme has been going on for more than 5 years now. By its very nature, in particular because a significant number of the studied stars have periods (much) longer than the time span during which we have followed them, it is not completed yet. However, it appears justified to report the results obtained so far, in view of their quantity and of their importance. Indeed, 29 new Ap stars with resolved magnetically split lines have been found, and more than 750 measurements of the mean magnetic field modulus of such stars have been performed. The results presented in this paper correspond to the observations that have been performed for this programme until end of August 1995.
Some partial, preliminary reports on this project have
already been given in previous publications. Mathys (1990;
hereafter referred to as Paper I) had discussed the physics of the formation
of the spectral line 
, from which we diagnose the field
modulus. He also had reported the discovery of magnetically resolved
lines in 3 stars: HD 55719, HD 94660, and HD 116458, and confirmed
Scholz's (1979) suspicion for the presence of resolved lines
in HD 201601. Mathys & Lanz (1992; Paper II) had announced
the presence of resolved magnetically split lines in 6 additional stars:
HD 2453, HD 9996, HD 18078, HD 50169, HD 137949, and HD 192678. They had
also discussed the relative magnetic intensification of the 
lines
and 
. The discovery of 4 more stars
with magnetically resolved lines (HD 14437, HD 110066, HD 116114, and
HD 134214) had first been reported by Mathys et al. (1993;
Paper III).