The invention relates to a gas bearing of a rapidly rotating shaft, whose end supports a tool, in particular to a gas bearing of a rapidly rotating shaft, whose end supports a polygon mirror (27) for a spindle of an optical application. To provide radial support along the shaft (3), gas bearings are arranged in a housing (5), whereby a first gas bearing (9) and a third gas bearing (8) are positioned concentrically in relation to one another and a second gas bearing (2), which is located midway between the first gas bearing (9) and the third gas bearing (8), is mounted in an eccentrically offset manner to the first gas bearing (9) and the third gas bearing (8). The invention is also provided with an adjusting device (1) for increasing the eccentric offset of the second gas bearing (2) as the rotational speed of the shaft (3) increases.