KING EDWARD III of England (1312-1377) has, back to the time of Charlemagne, about 1000 perches on his family tree. Of course in the relatively closed world of medieval royalty, many names on that tree appear more than once; indeed the repetition of ancestors conforms to a predictable pattern. A new study of the statistical properties of genealogical trees, using Edward III's pedigree as a case history, concludes that by going about 30 generations into your past, you and all your contemporaries will be related to everyone who lived then, at least to those who had offspring and who lived within that particular geographical or cultural realm. Bernard Derrida of the Ecole Normale Superieure in Paris (bernard.derrida@lps.ens.fr), Susanna Manrubia of the Max Planck Institute in Berlin, and Damian Zanette (Barlioche, Argentina), have discovered that the factors shaping the patterns of repetitions of individuals in family trees have traits in common with the forces that govern the behavior of granular materials and can, furthermore, be understood using the mathematical tools applied to a variety of phase transitions in physics. They expect their work to have applications in the study of population genetics and evolutionary biology. Derrida et. al., Physical Review Letters, 1 March 1999; view Edward's family tree at http://uts.cc.utexas.edu/~churchh/edw3chrt.html; see figure at Physics News Graphics )