The magnetic moments of the •£•" states at 1.610 MeV in 37 Ar and 1.380 MeV in 37 K were measured by differential spin-precession methods. The moments, together with the remeasured halflives, are /i --1.33(5)/ijv anc * '11/2 = 4.6(2) nsec for 37 Ar, and pi=+ 5.2(3)M A and T 1 / 2 = 10.5(5) nsec for the 37 K state. The prediction of the Sachs mirror theorem is shown to hold, and systematic trends in^-state moments of l/ 7 / 2 -shell nuclei are examined .The early development of the shell model was dependent, in part, on the desire to explain nuclear magnetic moment values. Although the moments rarely fall on the Schmidt limits, 1 the fact that most moments lie inside the lines and near them at the closed shell is an important indication of the model's validity. Explanation of the deviations of moments from the simple predictions should be an equally important means for checking more detailed calculations.