The orbits of the minor planets surrounding the 2 : 1, 3 : 1, 3 : 2 and 4 : 3 commensurabilities with Jupiter are examined to determine whether or not the critical argument in the disturbing function librates. It is found that for most of the minor planets at the 3 : 2 and 4 : 3 commensurabilities it does librate, and for most of those at the 2 : 1 and 3 : 1 commensurabilities it does not. A possible theory of the origin of the Kirkwood gaps suggested by these results is discussed.