The sleeve of a micrometer caliper displays the current distance between the anvil and the spindle, the locking mechanisms of the caliper, in quarter micrometer increments. These are acid-etched lines and numbers in the metal of the sleeve, which is revealed or concealed according to the contraction or expansion of the caliper jaws.
When the caliper's jaws are turned, the sleeve recedes into the thimble. The length of sleeve revealed shows the length of the space between the calipers. Once the method of reading this space is known, it becomes a very simple matter to measure anything the calipers can grip in micrometers.
The micrometers are measured out on the sleeve in quarters. Each individual micrometer receives its own acid-etched numeral while the quarters between are simple lines. This allows for extremely exacting measurements and for ease of reading, as the sleeve makes overlap and exact judgments a non-issue. All that need be learned is the way that the sleeve corresponds to the calipers themselves.
Without the sleeve, the calipers would be hopelessly difficult to measure by sight, as micrometers are too small for human eyes to readily distinguish in relation to a graded scale. The sleeve is a convenient mechanical solution to a difficult sensory problem.