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.
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Notes
I have used the modern notion of an element of surface to accommodate the fact that the force on a surface varies with its depth. Stevin recognized this fact and dealt with the variation in height by employing converging series in an ingenious way. Calculus had not yet been invented, of course, and Stevin himself did not employ the term “element” in the way I have done to summarise the essence of his position for the modern reader.
References
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The evolution of the science of hydrostatics in the seventeenth century is described in historical detail in Alan F. Chalmers, One Hundred Years of Pressure: Hydrostatics from Stevin to Newton (Dordrecht: Springer, 2017). Here I extract and describe the main message in a way that I hope will appeal to physicists.
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Alan Chalmers is an Honorary Senior Research Fellow in the School of History and Philosophy of Science at the University of Sydney, having joined that institution in 1971 with a PhD from the University of London on the introduction of the displacement current into electromagnetism. He is the author of four books and over sixty journal articles on the history and philosophy of the physical sciences.
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Chalmers, A. How Pressure Became a Scalar, Not a Vector. Phys. Perspect. 20, 165–179 (2018). https://doi.org/10.1007/s00016-018-0221-3
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DOI: https://doi.org/10.1007/s00016-018-0221-3
Keywords
- Hydrostatics
- pressure
- scalar
- vector
- Isaac Newton
- Robert Boyle
- Blaise Pascal
- Simon Stevin