1. Australian Aboriginal relationship terminologies can only (or best) be seen as structured according to patri-sequences (patrilines), in terms of which alliance properties can be expressed. This assumption stems from the pervasive influence of Radcliffe-Brown's The Social Organization of Australian Tribes (1931) and Elkin's The Australian Aborigines (latest edition 1964). Ruhemann (1945), by contrast, has demonstrated the utility of viewing these systems in terms of matri-sequences as well as patri-sequences; her contribution, however, has been largely ignored. RadcliffeBrown's Murngin analysis (1951) is also carried out with the aid of matrisequences, but these are regarded simply as diagrammatic devices with no necessary ethnographic validity. Finally, Berndt's representation of the same system (1955) contains matri-sequences, but these are not systematically described in his text (see Radcliffe-Brown 1956). 2. In societies with prescriptive marriage, alliance categories are identical, or at least isomorphic, with descent groups or local aggregates of kinsmen. Maybury-Lewis (1965) and, recently at least, Needham (1964, 1967) have proceeded without this assumption, but the overwhelming mass of the literature on elementary structures takes it for granted. This means, in the case at hand, that formal properties of alliance in northeast Arnhem Land are viewed largely in terms of patri-categories (see preceeding assumption), since there are patrilineal descent groups but no matrilineal descent groups or preference for uxorilocal residence. 3. Prescriptive marriage systems cannot be viewed as symmetric if they can be seen in terms of at least three patri-sequences with continuous asymmetric relationships with each other. Lane (1961) has challenged this, though her arguments have not been generally accepted and so far lack detailed published ethnographic support (but see Shapiro 1967a, 1967c, 1967d, 1969a, 1969b:Chapter 8). This assumption forms the basis of the attempts by Leach (1961:68-72), Berndt (1955), and others
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