Analysis of Doubts in the Artificers' Record

If the wood were too thin—not even reaching half the necessary thickness—then the calculation must have only accounted for the part of the spoke’s handle that enters the chiseled hole. However, the actual stem of the spoke tenon zai: the part of the spoke that is shaped to fit into the hub is surely not limited to this measurement alone.

In ancient times, a hub held thirty spokes, and the width of each spoke's body was less than one inch.

Therefore, when the text describes using a le le: a ratio of one-third of the circumference to carve shao: the act of hollowing or shaping it, the calculation implies using two-thirds of the volume for the solid wood rou: literally "flesh," referring to the structural wood of the hub and one-third for the hollow interior hu: literally "the pot," the central cavity. This hollow "pot" is the space that receives the axle.

The text below states: "Divide the length of the hub into five parts; remove one part to determine the width of the middle-hub xian: the widest part of the hub where the spokes are inserted, and remove three parts to determine the width of the hub-end zhi: the tapered outer end of the hub."

This indicates that the interior of the "pot" is large on the inside and tapers to be smaller on the outside. Only at the specific point on the exterior where the spokes and tenons are situated does the interior cavity measure exactly one-third of the total.

Generally speaking, the entire hollow space can be called the "hub." This is what the later scripture means when it refers to "measuring the hub with lacquer" original: 量其轂以漆 (liang qi gu yi qi); this refers to a method of checking the volume or seal of the hub using liquid lacquer. However, to be more precise, the specific section on the exterior where the spokes and tenons are joined is also referred to as the "hub" in the context of this specific passage.

The Rule of Five Parts

Divide the length of the hub into five parts: remove one to determine the middle-hub original: 賢 (xian); remove three to determine the hub-end original: 軹 (zhi).