Abstract: In a precision machine, such as a coordinate measuring machine or a machine tool in which a carriage rides along a rail, a gas bearing for applying a constant preload force to a bearing shoe over a range of relative movement between said bearing shoe and the carriage to accommodate imperfections and non-parallelism in the rail. The constant preload force is provided by a disc spring, which may be a Belleville spring. A preferred spring has a free height to thickness ratio in the range of from about 1.35:1 to about 1.6:1. The gas bearing of this invention is used in opposed relation with another gas bearing.