  During the past decade the dynamical importance of magnetic fields in
molecular clouds has been increasingly recognized, as observational evidence
has accumulated. However, how a magnetic field affect star formation is still
unclear. Typical star formation models still treat a magnetic fields as an
isotropic pressure, ignoring the fundamental property of dynamically important
magnetic fields: their direction. This study builds on our previous work which
demonstrated how the mean magnetic field orientation relative to the global
cloud elongation can affect cloud fragmentation. After the linear mass
distribution reported earlier, we show here that the mass cumulative function
(MCF) of a cloud is also regulated by the field orientation. A cloud elongated
closer to the field direction tends to have a shallower MCF, in other words, a
higher portion of the gas in high density. The evidence is consistent with our
understanding of bimodal star formation efficiency discovered earlier, which is
also correlated with the field orientations.
