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Résumé : We have observed coherence among the four magnetic sublevels of freely precessing $^{21}\mathrm{Ne}$ for times of 4.5 h. This has allowed direct detection of the quadrupole component of coherence relaxation and a test of linearity of quantum mechanics. The quadrupole component of relxation is evident in the different relaxation rates for the three lines of the NMR spectrum. Nonlinear corrections to quantum mechanics are found to be less than 1.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}26}$ of the binding energy per nucleon of $^{21}\mathrm{Ne}$.