We present initial results from the Filaments Extremely Long and Dark: A Magnetic Polarization Survey (FIELDMAPS) of far-infrared polarization in ten of the largest known filaments in the Milky Way. These observations were obtained at 214 µm with the HAWC+ camera on the Stratospheric Observatory for Infrared Astronomy (SOFIA). They provide the highest resolution measurements to date of the magnetic field in these dense filamentary structures, also described as the “bones” of our Galaxy. Following our previous study of the G47 cloud (Stephens et al. 2022), we use the Davis-Chandrasekhar-Fermi (DCF) technique, combined with ancillary spectroscopic data of dense gas tracers (e.g., NH3) in each bone, to quantify the magnetic field amplitude across these filaments. Specifically, we experiment with modified DCF techniques such as fitting the Angular Dispersion Function (ADF) along the spine of the filaments. We present the first description of the polarization structure of all ten bones, their angular relation of the polarization direction to the bone axis, their typical mass to flux ratios (MFRs), and the relation of the MFR to their column density and level of star formation. We compare these results to those published for G47, where we found evidence that the filament is magnetically subcritical (i.e., the magnetic field is sufficient to support the cloud against gravitational collapse) except in regions of active star formation.