constant than that of air, and given the same height difference, the pressure differences in water are approximately equal at any height. Hydrostatic paradox The barometric formula depends only on the height of the fluid chamber, and not on its width or length. Given a large enough height, any pressure may be attained. This feature of hydrostatics has been called the hydrostatic paradox. As expressed by W. H. Besant, Any quantity of liquid, however small, may be made to support any weight, however large. The Dutch scientist Simon Stevin was the first to explain the paradox mathematically. In 1916 Richard Glazebrook mentioned the hydrostatic paradox as he described an arrangement he attributed to Pascal: a heavy weight rests on a board with area resting on a fluid bladder connected to a vertical tube with cross-sectional area α. Pouring water of weight down the tube will eventually raise the heavy weight. Balance of forces leads to the equation Glazebrook says, "By making the area of the board considerable and that of the tube small, a large weight can be supported by a small weight of water. This fact is sometimes described as the hydrostatic paradox." Demonstrations of the hydrostatic paradox are used in teaching the phenomenon. In the context of Earth's atmosphere If one is to analyze the vertical pressure variation of the atmosphere of Earth, the length scale is very significant (troposphere alone being several kilometres tall; thermosphere being several hundred kilometres) and the involved fluid (air) is compressible. Gravity can still be reasonably approximated as constant, because length scales on the order of kilometres are still small in comparison to Earth's radius, which is on average about 6371 km, and gravity is a function of distance from Earth's core. Density, on the other hand, varies more significantly with height. It follows from the ideal gas law that where is average mass per air molecule, is pressure at a given point, is the Boltzmann constant, is the temperature in kelvins. Put more simply, air density depends on air pressure. Given that air pressure also depends on air density, it would be easy to get the impression that this was circular definition, but it is simply interdependency of different variables. This then yields a more accurate formula, of the form where is the pressure at height , is the pressure at reference point 0 (typically referring to sea level), is the