The principal Hugoniot jump relations can be cast in a differential form that relates the Gru¨neisen constant, isentropic bulk modulus, pressure, particle velocity, and shock velocity to each other through an algebraic equation. From this relation I show the general features of the Hugoniot, including a low pressure and a high pressure linear region with a connecting break in slope, limiting forms, and insensitivity to atomic shell structure. The value of the slope for high pressures is explained. The excellent agreement with data is presented. ©1998 American Institute of Physics.