  The P1/P2 period ratio of transversal loop oscillations is currently used for
the diagnostics of longitudinal structuring of coronal loops as its deviation
from 2 is intrinsically connected to the density scale-height along coronal
loops and/or the sub-resolution structure of the magnetic field. The same
technique can be applied not only to coronal structures, but also to other
oscillating magnetic structures. The oscillations in magnetic structures are
described by differential equations whose coefficients depend on the
longitudinal structure of the plasma. Using a variational principle written for
the transversal component of the velocity vector, developed earlier by McEwan
et al. (2008), we investigate how the different temperature of the environment
compared to the temperature of the magnetic structure will influence the P1/P2
ratio for typical coronal and prominence conditions. The possible changes are
translated into quantities that are used in the process of remote plasma
diagnostics in the solar atmosphere.
