M. Cohn and A. Lempel [J. Comb. Theory, Ser. A 13, 83-89 (1972; Zbl 0314.05005)] showed that if \(\tau \in S_ n\) is an n-cycle and \(\sigma \in S_ n\) is a product of disjoint transpositions, then the number of orbits of \(\sigma\) \(\tau\) is one more than the nullity of a certain matrix over GF(2), obtained as an incidence matrix for carefully chosen chords of a circle. Here, a new proof is given, based on the study of a certain boolean measure on the boolean algebra of subsets of the circle.