1. This paper proposes some modifications of the family-tree diagram traditionally used to indicate genetic relationships in comparative linguistics. The flaws in the traditional diagram have long been recognized; it would be difficult to improve on Bloomfield's discussion of the subject in Language §§18.9–12. Although contemporary linguists have rejected the theory on which the branching diagram was originally based, they have not taken the logical next step of trying to improve the diagram itself so as to make it compatible with the revised theory. I shall attempt to show here that it is not necessary to reject branching diagrams entirely, but that it is possible to modify the traditional diagram so that it presents a truer and clearer picture of linguistic history as it is conceived at the present time. There are probably many possible ways in which we could depict linguistic history, and I do not attempt to do justice to all possibilities here; I hope only to show some variants on the traditional diagram which may lead to a better understanding of the potential use of such devices. First, a word on the role of diagrams in historical work. The diagrams which are presented here are not intended as theoretical models, but only as visual aids. Such diagrams are at best shorthand representations of the history of a group of languages, showing in a single picture the interrelations of the whole group. The primary danger to be avoided is that of overliteral interpretation; as Bloomfield says,