  The big majority of the reported measurements of the stellar magnetic fields
that have analysed spectropolarimetric data have employed the
least-square-deconvolution method (LSD) and the first-order moment approach. We
present a series of numerical tests in which we review some important aspects
of this technique. First, we show that the selection of the profile widths,
i.e. integration range in the first-order moment equation, is independent of
the accuracy of the magnetic measurements, meaning that for any arbitrary
profile width it is always possible to properly determine the longitudinal
magnetic field. We also study the interplay between the line depth limit
adopted in the line mask and the normalisation values of the LSD profiles. We
finally show that the rotation of the stars has to be considered to correctly
infer the intensity of the magnetic field, something that has been neglected up
to now. We show that the latter consideration is crucial, and our test shows
that the magnetic intensities differ by a factor close to 3 for a moderate fast
rotator star with vsini of 50 km/s. Therefore, it is expected that in general
the stellar magnetic fields reported for fast rotators are stronger than what
was believed. All the previous results shows that the first-order moment can be
a very robust tool for measurements of magnetic fields, provided that the weak
magnetic field approximation is secured. We also show that when the magnetic
field regime breaks down, the use of the first-order moment method becomes
uncertain.
