[1] In machine design, some components are particularly sensitive to angular errors.
For example, slight deviations from parallelism of the spindle axis of a lathe to the tool motion along the bed of the machine can lead to relatively large (undesired) taper along the part (i.e. a non-cylindrical part).
Vernier calipers are not free from Abbe error, while screw gauges are free from Abbe error.
[2] Abbe error can be detrimental to dead reckoning.
is the distance, sometimes called the Abbe offset.