Absolute dating techniques were not available to him (radiocarbon dating wasn't invented until the 1940s); and since they were separately excavated graves, stratigraphy was no use either.Petrie knew that styles of pottery seemed to come and go over time--in his case, he noted that some ceramic urns from the graves had handles and others had just stylized ridges in the same location on similarly shaped urns.He assumed that the change in styles was an evolutionary one, and, if you could quantify that change, he surmised it might be used to indicate which cemeteries were older than others.
Overview of Methods Superposition Stratigraphy Dendrochronology Radiocarbon C14 Radiometric Dating Methods Obsidian Hydration Dating Paleomagnetic/Archaeomagnetic Luminescence Dating Methods Amino Acid Racemization Fission-track Dating Ice Cores Varves Pollens Corals Cation Ratio Fluorine Dating Patination Oxidizable Carbon Ratio Electron Spin Resonance Cosmic-ray Exposure Dating This is an excellent overview of dating methodologies, and is a chapter in a textbook on Archaeology.
You may find it useful for the clear definitions, and for excellent links on a variety of topic.
However, human beings love to see factual precision, and we want to know how old something is.
Please remember that all dating methods, even those termed "absolute," are subject to margins of error. That is a very small amount of possible error range. Modern studies almost always use two or more methods to confirm dating work and to build confidence in the results obtained.
To see how we actually use this information to date rocks, consider the following: Usually, we know the amount, N, of an isotope present today, and the amount of a daughter element produced by decay, D*.