Since the beginnings of historical linguistics, the family tree has been the most widely accepted model for representing historical relations between languages. While this sort of representation is easy to grasp, and allows for a simple, attractive account of the development of a language family, the assumptions made by the tree model are applicable in only a small number of cases: namely, when a speaker population undergoes successive splits followed by complete loss of contact. A tree structure is unsuited for dealing with dialect continua, and language families that develop out of dialect continua ("linkages", as Ross 1988 calls them); in these situations, the scopes of innovations (their isoglosses) are not nested, but rather they constantly intersect, so that any proposed tree representation is met with abundant counterexamples. In this paper, we define "Historical Glottometry", a new method capable of identifying and representing genealogical subgroups even when they intersect. We apply this glottometric method to a specific linkage, consisting of 17 Oceanic languages spoken in northern Vanuatu.