A spindle apparatus includes a rotatable first spindle (5, 32) to which a tool can be attached. The first spindle is supported in a base with high precision using an air hydrostatic bearing. The spindle apparatus further includes a second spindle (6, 33) capable of rotation about an axis substantially aligned with the axis of the first spindle, first connection means for electrically connecting a base side and the second spindle, and second connection means for electrically connecting the first spindle and the second spindle. Electrical connection between the base side and the first spindle is carried out via the first and second connection means. The first connection means is, for example, a brush (15, 36). The second connection means has a degree of mechanical freedom and is, for example, a flexible electrical wire (17, 39) or a helical spring (51).