Elliptical constructions occur when you write two related independent clauses, typically separated by a semicolon, and you omit a word or words from the second one. The way you punctuate this kind of construction depends on how much you omit. In the following sentence, the words “servants” and “chamber” are omitted in the portion of the sentence after the semicolon:

The king’s servants sleep in the eastern chamber; the queen’s sleep in the western.

However, if you also omit the verb “sleep” in the portion after the semicolon, a comma would be required after “queen’s”:

The king’s servants sleep in the eastern chamber; the queen’s, in the western.