Is this the proper use of a semi-colon: "The majority of them sit a few inches from the other; only a few overlapping."?
A comma would be more appropriate.
A semicolon signifies a shift of thought within a sentence. "The majority of them sit a few inches from the other; some of them have knives." The sentence in the example is simply a continuation of an established line of thought and a comma would be more appropriate.
A colon (although you didn't ask) is a more abrupt halt within a sentence, usually used to show one or more examples of the idea that preceded it. "The majority of them sit a few inches from each other: some on boxes, some on chairs."
Lynn Truss. author of Eats, Shoots and Leaves , compares the comma with a musical quarter note, a semicolon with a half note, a colon with a three-quarter note and a period/full stop with a whole note.