# Stevin’s Hydrostatics

A key starting point is Stevin’s attempt to move beyond the science of weight with his *Elements of Hydrostatics* and its short sequel, *The Practice of Hydrostatics.* I have analysed and evaluated his theory in detail elsewhere. Here I summarise and exploit the conclusions to which I have been led.^{[1]}

On the face of it, Stevin’s hydrostatics consists of a body of theorems derived from unproblematic postulates. A not over-generous summary of the content of those theorems, sometimes referred to as Stevin’s law, is as follows: Normal to any solid surface element bounded by a liquid there is a force that is equal to the weight of a prism of the liquid whose cross section is equal to the area of the surface element in question and whose height is equal to the depth of the surface element beneath the liquid surface. This claim is correct from a modern point of view if we limit ourselves to the forces in liquids stemming from their own weight.

A close analysis of Stevin’s derivation of his theorems reveals that they do not in fact follow from his postulates. Those postulates relate only to forces acting in a vertical direction, whether they are weights bearing down or the vertically acting resistances offered by liquids to them. They cannot yield the isotropic forces implicit in Stevin’s law as deductive consequences. When, for instance, Stevin derives the horizontal force exerted by a liquid on a vertical plane he relies on two assumptions that he makes without signalling the fact and which are not consequences of his postulates. He assumes that the liquid does exert a force normal to a vertical plane and he assumes that the strength of that force on an element of a vertical plane at some particular depth in the liquid is equal to the force normal to an element of a horizontal plane of the same area and at the same depth.^{[2]} In effect, Stevin, here and elsewhere in his hydrostatics, simply assumes that the forces with which a liquid presses against a solid surface are independent of the orientation of that surface.

There is no doubt that Stevin, who, amongst other things, was a hydraulic engineer *in the Netherlands,* was aware that water presses horizontally against a dyke or a lock gate and that wine issues horizontally from a leak in the side of a wine cask.^{[3]} Such recognitions notwithstanding, the horizontal pressing of a liquid was puzzling from the point of view of the science of weight, and continued to be so for decades after 1586. How can a liquid press sideways given that its weight acts vertically downwards? The horizontal component of weight is zero! To the extent that there is a puzzle here, Stevin does nothing to help the situation by feeding in the puzzling data as an assumption, and, what is more, one that is unheralded. Stevin clearly had an intuitive grasp of the fact that liquids press equally in all directions, and this is most evident in his presentation in the *Practice of Hydrostatics.* However, he was unable to explicate this in the *Elements of Hydrostatics* because in that work he was intent on deriving his theorems from postulates that could be granted at the outset and key aspects of the behaviour of liquids went beyond what could be so granted.

Stevin’s practical experience with liquids somehow guided him to hydrostatic theorems that correctly describe the phenomena. But he fell short of formulating a theory that captured mathematically the distinction between liquids and solids that would take him beyond the science of weight to a science of hydrostatics.

- [1] English translations of Stevin’s works on hydrostatics, together with the Dutch originals are inDijksterhuis, Principal Works of Stevin, op. cit., pp. 393-501. A detailed analysis of Stevin’shydrostatics is given in Alan Chalmers, “Qualitative Novelty in Seventeenth-century Science:Hydrostatics from Stevin to Pascal” in Studies in History and Philosophy of Science, 51, 2015, pp. 1-10.
- [2] Stevin’s, admittedly mathematically ingenious, deduction is in Dijksterhuis, Principal Works ofStevin, op. cit., pp. 421-423. The details of my critique are in Chalmers, “Qualitative Novelty” op.cit., pp. 3-9.
- [3] Stevin explicitly discussed the force exerted on a lock gate. See Dijksterhuis, Principal Works ofStevin, op. cit., p. 497.