In this paper, the authors evaluated the angular motion for air spindle by way of vector method which has been developed by the authors. From two vectors of radial displacement at the same rotating angle on two planes of different height, the directional cosines of rotating axis are calculated. It is made clear that this directional cosine method is able to confirm the behavior of anguler motion of the air spindle. Furthermore this paper proposes an information on the tilting motion of spindle axis and the spacial phase delay of rotating axis.