  We propose to accurately determine the orbital magnetic moment of the
electron by measuring, in a Magneto-Optical or Ion trap, the ratio of the Lande
g-factors in two atomic states. From the measurement of (gJ1/gJ2), the quantity
A, which depends on the corrections to the electron g-factors can be extracted,
if the states are LS coupled. Given that highly accurate values of the
correction to the spin g-factor are currently available, accurate values of the
correction to the orbital g-factor may also be determined. At present, (-1.8
+/- 0.4) x 10-4 has been determined as a correction to the electron orbital
g-factor, by using earlier measurements of the ratio gJ1/gJ2, made on the
Indium 2P1/2 and 2P3/2 states.
