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We report the results of 3D simulations of the trajectories of ultra-highenergy protons and Fe nuclei (with energies $E = 4 \times 10^{19}$ and $2.5\times 10^{20} eV$) propagating through the galactic magnetic field from thesources to the detector. A uniform distribution of anti-particles isbacktracked from the detector, at the Earth, to the halo of the Galaxy. Weassume an axisymmetric, large scale spiral magnetic field permeating both thedisc and the halo. A normal field component to the galactic plane ($B_z$) isalso included in part of the simulations. We find that the presence of a largescale galactic magnetic field does not generally affect the arrival directionsof the protons, although the inclusion of a $B_z$ component may causesignificant deflection of the lower energy protons ($E = 4 \times 10^{19} $eV). Error boxes larger than or equal to $\sim 5^{\circ}$ are most expected inthis case. On the other hand, in the case of heavy nuclei, the arrivaldirection of the particles is strongly dependent on the coordinates of theparticle source. The deflection may be high enough ($> 20^{\circ}$) as to makeextremely difficult any identification of the sources unless the real magneticfield configuration is accurately determined. Moreover, not every incomingparticle direction is allowed between a given source and the detector. Thisgenerates sky patches which are virtually unobservable from the Earth. In theparticular case of the UHE events of Yakutsk, Fly's Eye, and Akeno, they comefrom locations for which the deflection caused by the assumed magnetic field isnot significant.Comment: LaTeX + 2 postscript figures - Color versions of both figures (highly  recommended) available via anonymous ftp at  ftp://capc07.ast.cam.ac.uk/pub/uhecr_gmf as fig*.g

Deflection of Ultra–High‐Energy Cosmic Rays by the Galactic Magnetic Field: From the Sources to the Detector