How Pressure Became a Scalar, Not a Vector

Abstract

The gradual emergence of a science of hydrostatics during the course of the seventeenth century is testament to the fact that a technical concept of pressure that was up to the task was far from obvious. The first published version of a theory of hydrostatics containing the essentials of the modern theory appeared in book 2 of Isaac Newton’s Principia. Newton derived the propositions of hydrostatics from a definition of a fluid as a medium unable to withstand a distorting force. Newton’s reasoning required that pressure be understood as a force per unit area acting on either side of imaginary planes within the body of a fluid. For a fluid in equilibrium, the forces at some location within a fluid are independent of the orientation of such planes. As Newton came to realize, within the body of a liquid, pressure acts equally in all directions so that there is no resultant pressing in any direction. Pressure has an intensity but not a direction. In modern terms, it is a scalar, not a vector. Although earlier scholars such as Simon Stevin, Blaise Pascal, and Robert Boyle helped set the scene for Newton’s innovations, they were unable to transcend the common sense of pressure as a directed force acting on the solid surfaces bounding a fluid.