We report the results of resonant x-ray diffraction at the sulfur K -edge performed upon free-standing films of a thiobenzoate liquid-crystal compound. Our data provide the first direct structural evidence of distinct periodicities in several chiral Sm-C phases, including 2-layer, 3-layer, and 4-layer superlattices in Sm-C{sup *}{sub A} , Sm-C{sup *}{sub FI1} , and Sm-C{sup *}{sub FI2} , respectively. In Sm-C{sup *}{sub {alpha} } , periodicity incommensurate with the layer spacing was detected. The racemic compound version was also studied. The results are consistent with a {open_quotes}clock model{close_quotes} of the Sm-C{sup *} variant structures. {copyright} {ital 1998} {ital The American Physical Society}