  There is increasingly strong observational evidence that slow magnetoacoustic
modes arise in the solar atmosphere. Solar magneto-seismology is a novel tool
to derive otherwise directly un-measurable properties of the solar atmosphere
when magnetohydrodynamic (MHD) wave theory is compared to wave observations.
Here, MHD wave theory is further developed illustrating how information about
the magnetic and density structure along coronal loops can be determined by
measuring the frequencies of the slow MHD oscillations. The application to
observations of slow magnetoacoustic waves in coronal loops is discused.
