A coreless log of convolutely wound web material is formed by directing the web around an applicator roller that is in contact with a first surface of the web. An additive is transferred from a supply roller to the applicator roller over a first distance of the web and stopped over a second distance of the web. The web is directed around at least one further roller that is in contact with the second surface of the web that is opposite the first surface. The web is then wound around an elongated mandrel. The first distance of the web comprises a first set of windings nearest the center of the log, and the second distance of the web comprises a second set of windings wound around and extending radially outward from the first set of windings. The mandrel may then be removed to form the coreless log.