Tolerances between ±0.004 in (±0.10 mm) and ±0.001 in (±0.025 mm) are where the challenge begins rising. In deep holes with tolerances this tight, the limiting factor is just as often the geometric constraint as the size constraint. In other words, it may be easy to hold the diameter within .002" at any diametrical measurement point, but difficult to hold the cylindricity of the hole to within a zone delimited by the .002" constraint, across more than 5 diameters of hole depth (depth measured in terms of diameter:depth aspect ratio). For highest-precision applications, tolerances can generally be held within ±0.0005 in (±0.013 mm) only for shallow holes. In some cases tolerances as tight as ±0.0001 in (±0.0038 mm) can be held in shallow holes, but it is expensive, with 100% inspection and loss of nonconforming parts adding to the cost. Grinding, honing, and lapping are the recourse for when the limits of boring repeatability and accuracy have been met. Surface finish (roughness) in boring may range from 8 to 250 microinches, with a typical range between 32 and 125 microinches. Sometimes a part may require higher accuracy of form and size than can be provided by boring. For example, even in optimized boring, the amount that the diameter varies on different portions of the bore is seldom less than 3 micrometre (.0001 inches, "a tenth"), and it may easily be 5 to 20 micrometre (.0002-.0008 inches, "2 to 8 tenths"). Taper, roundness error, and cylindricity error of such a hole, although they would be considered negligible in most other parts, may be unacceptable for a few applications. For such parts, internal cylindrical grinding is a typical follow-up operation. Often a part will be roughed and semifinished in the machining operation, then heat treated, and finally, finished by internal cylindrical grinding. The limitations of boring in terms of its geometric accuracy (form, position) and the hardness of the workpiece have been shrinking in recent decades as machining technology continues to advance. For example, new grades of carbide and ceramic cutting inserts have increased the accuracy and surface quality that can be achieved without grinding, and have increased the range of workpiece hardness values that are workable. However, working to tolerances of only a few micrometres (a few tenths) forces the manufacturing process to rationally confront, and compensate for, the fact that no actual workpiece is ideally rigid and immobile. Each time