Hydrostatic Paradox
   The hydrostatic paradox arises from our failure to accept, at first sight, the conclusion published by Blaise Pascal in 1663: the pressure at a certain level in a fluid is proportional to the vertical distance to the surface of the liquid. Pascal's Vases are well known illustrations of the paradox, but the two demonstrations on this page are little known. 

   The hydrostatic bellows apparatus above (at Transylvania University) and to the right (from the 1871 edition of Denison Olmsted's Natural Philosophy text)  were sold by many 19th century equipment manufacturers. The 1860 Ritchie catalog offered this model "of improved form and construction; mahogany, twelve inches square, with patent leather sides lined with vulcanized rubber; brass socket and three-way water cock; brass and glass tubes with brass screw connections; funnel, ...$10.00"

   It must have been a great surprise to see a 150 pound student supported by a column of water reaching only 2.4 ft above the level of the platform.
    The apparatus at the left is is "Ritchie's Illustration of the Hydraulic Press; mahogany base with a sliding platform supported by brass pillars, with a weight; upon the base is placed a bellows-shaped rubber bag, connected by a tube to a globular bag fitted with a cap and cork. Fill the globe with water, and elevate it; the pressure of the column will force the water into the bellows, raising the weight; lower the globe, and the weight will force the water back into it... $12.00".

   Middlebury College's surviving example of this apparatus is in remarkably good condition after one hundred and more years. It needs only the replacement of rubber parts to make it work once more. 
    This version of the hydrostatic paradox at the right was in storage at the museum at the United States Military Academy at West Point when I saw it in February 2000. 

   The same apparatus, shown at the left, was on display in the Garland Collection of Classical Physics Apparatus at Vanderbilt University when I visited it in March 2001. 

   The apparatus is listed in the 1865 Deleuil catalogue as a device to show that all liquid-filled columns exert pressure independently of each other.  The apparatus cost 40 francs, or $10.00.

   Today I would fill each column with a liquid of a different density, with water filling the central column and reservoir. The taps would then be slowly opened, and liquids added to keep the interfaces at the same level. 
   The Millington./Barnard Collection at the University of Mississippi Museum has an example of the Hydrostatic Paradonx identical to the ones at West Point and Vandcerbilt.

REFERENCE: Thomas B. Greenslade, Jr., "Nineteenth Century Textbook Illustrations (XXII), The Hydrostatic Paradox". Phys. Teach., 16, 228-229 (1978)

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