Abstract
In this thesis,we write down the Dirac equation with the third-order expension of the metric tensor.The curvature effects give out the Gyro-Gravitational Ratio. Via three succesive Foldy-Wouthuysen transformation, we obtain the Dirac equation in weak field, slow motion limit; and further,calculate the geodesic deviation equation, compare with Papapetrou equation. Finally,we will discuss the Gyro-Gravitational Ratio.