To study the rigidity of the Pacific and Farallon plates between 72 and 35 Ma, we analyzed the magnetic anomalies and fracture zones in the Pacific Ocean between longitudes 125 ¿W--180¿ and latitudes 43 ¿S--60 ¿N. A set of consistent rotations indicates that the Pacific and Farallon plates between the Pioneer and Agassiz fracture zones were rigid plates between 72 and 35 Ma. Thus the location of a missing Tertiary boundary, within the Pacific or Antarctic plates, is restricted to be south of latitude 43 ¿S. The Farallon plate broke into two plates at the time of the change in the Pacific-Farallon spreading direction north of the Pioneer and Mendocino fracture zones, sometime between 59 and 49 Ma. The northern fragment, termed the Vancouver plate, was subducted beneath most of North America. We present rotations and uncertainties for the histories of motion of the Pacific and Kula plates from anomaly 32 to anomaly 25, of the Pacific and Vancouver plates from anomaly 21 to anomaly 13, and of the Pacific and Farallon plates from anomaly 32 to anomaly 13. ¿ American Geophysical Union 1988