Abstract: An improved shaft seal for sealingly and rotatably mounting a torque-transmitting shaft within the pressurized housing of a pump. Generally, the shaft seal comprises a seal ring which is sealingly mounted within the housing, and a runner ring which is sealingly mounted around the shaft. Both the seal ring and the runner are preferably formed from 98% pure, hot-pressed silicon nitride. Additionally, the sealing surface of the seal ring is preferably radially tapered between about 635 and 645 microradians around its outer periphery, and between about 210 and 230 microradians around its inner periphery. The pressurized fluid within the housing enters the annular space between the two sealing surfaces and creates a flowing film of fluid upon which the two sealing surfaces may "ride" without frictionally engaging one another.