What is the part of a lathe carriage that bridges across the bed to carry the cross slide and tool rest?

The correct answer is "D. Saddle." The saddle is the component of a lathe carriage that bridges across the bed and serves as the support for both the cross slide and the tool rest. Its primary function is to provide stability and precision while allowing lateral movement, which is essential for producing accurate cuts on materials being machined.

The saddle must be robust to withstand the forces generated during machining and is typically designed to fit securely on the lathe bed, ensuring proper alignment. This positioning also allows the cross slide to move smoothly along the saddle, which is crucial for operational efficiency and accuracy in the machining process.

The other choices are related components of a lathe but perform different functions. The apron is attached to the front of the saddle and contains the mechanisms for the lathe's automatic feed. The compound rest is a part of the lathe that allows for angular adjustments and is mounted on top of the cross slide, not directly bridging the bed. The automatic feed refers to the mechanism for automatically advancing the cutting tool, rather than a supporting structure. Each of these parts plays a critical role in the functionality of a lathe but doesn't fulfill the specific role that the saddle does in bridging the bed and supporting the cross slide and tool rest.