  Other devices employed to fashion rational formulae involved the notion of a radical, a grouping of elements that persisted through a range of chemical changes so that they play a role in organic chemistry akin to that of elements in inorganic chemistry. Series of compounds could be understood in terms of additions, for example to the methyl radical, CH3, or to the ethyl radical, C2H5, and so on. ‘Homologous series’ of compounds could be formed by repeatedly adding CH2 to the formulae for such radicals so that the properties, and indeed the existence, of complex compounds could be predicted by analogy with simpler ones. Another productive move involved the increasing recognition that the action of acids needed to be understood in terms of the replacement of hydrogen. Polybasic acids were recognised as producing two or more series of salts depending on whether one, two or more hydrogens are replaced. Yet another important move involved the demand that rational formulae capture certain asymmetric compounds, such as methyl ethyl ether, CH3C2H5O, as distinct from methyl ether, (CH3)2O, and ethyl ether, (C2H5)2O. By 1860, the idea of tetravalent carbon atoms that could combine together in chains was added. By that stage, the demand that rational formulae reflect a wide range of chemical properties had resulted in a set of formulae that was more or less unique. The under-determination problem that had blocked the way to the establishment of unique formulae and atomic weights had been solved by chemical means.