
Room four of the Boerhaave Museum, Leiden, which shows some of the original instrumentation of the Leiden University research program: Some type of early telescope, large globes, tiny pocket globe, a table sized planetarium, star atlas, vacuum pumbs (1670-1730), several Magdeburg hemispheres, hydrometers, an aerometer, a hydrostatic bellows, a balance and steam pump, several table-top fountains all used to look into hydrostatic pressure, and capillary attraction, and models of three out of five of Archimedes' so called simple machines (lever, inclined plane, wedge, screw and wheel), several hydrostatic balances to demonstrate Archimedes' law and two tables of forces which demonstrate interactions of forces in a horizontal plane, among other devices. [3]

Room four of the Boerhaave Museum, Leiden, which shows some of the original instrumentation of the Leiden University research program: Some type of early telescope, large globes, tiny pocket globe, a table sized planetarium, star atlas, vacuum pumbs (1670-1730), several Magdeburg hemispheres, hydrometers, an aerometer, a hydrostatic bellows, a balance and steam pump, several table-top fountains all used to look into hydrostatic pressure, and capillary attraction, and models of three out of five of Archimedes' so called simple machines (lever, inclined plane, wedge, screw and wheel), several hydrostatic balances to demonstrate Archimedes' law and two tables of forces which demonstrate interactions of forces in a horizontal plane, among other devices. [3]

In thermodynamic schools, Leiden University, or “Leyden University” in archaic Dutch or “Leiden school”, historically, is the first of the so-called “school” of thermodynamic thought, tracing back, generally, to the experimental demonstration of Boerhaave’s law or volume expansion by heat of Dutch physician and chemist Herman Boerhaave along with kinetic energy experiments by Dutch physicist Christiaan Huygens, regarding inelastic collisions, and later by Dutch physicist-mathematician Willem Gravesande, involving brass balls and clay surfaces.

Overview
In the 1720s, a significant pre-thermodynamics school of influence was Leyden University, where Dutch physician and chemist Herman Boerhaave and Dutch physicist Willem Gravesande were famously conducting some of the first research on volume expansion by heat (ball and ring experiment), kinetic energy (ball and clay surface experiment), the general principle of volume expansion of bodies by heat (Boerhaave’s law), electricity (Leyden jar), among other noted scientific advances. As commented by French philosopher-physicist Voltaire, who acted as a scientific liaison between the Netherlands, France, and England, in a 1736 letter to the crown prince of Prussia (afterwards Frederick the Great), with whom he had entered into an active corresponds with:

“I am the town of two simple citizens, Boerhaave and Gravesande attract from four to five hundred strangers.”

The work of Boerhaave was carried over into later-to-come to predominance French science (Ecole polytechnique) school of thought, significantly in the work and caloric theory of Antoine Lavoisier (Elements of Chemistry, 1787). Students of Boerhaave include: Andrew Plummer, William Cullen, Joseph Black, and John Roebuck, and—through association with Black—James Watt—which can all products or precipitates, so to speak, of the Leyden school centered around Boerhaave. [20]


Left: a photo of what seems to be Dutch physicist-mathematician Willem Gravesande's brass ball clay surface kinetic energy experiments, shown at the Boerhaave Museum, Leiden, Netherlands. [3] Right: Dutch physicist-mathematician Willem Gravesande invented the "ball and ring experiment".

Kinetic energy experiment
In 1669, Dutch physicist Christiaan Huygens determined that the quantity of the mass of an object multiplied by its velocity squared mv² remains constant during perfectly elastic collisions, such as between steel balls.

In circa 1718, Dutch physicist-mathematician Willem Gravesande conducted his most-famous experiment in which he allowed brass balls to be dropped (or rolled down a ramp) with varying velocity onto a soft clay surface. Gravesande found in his experiments that a ball with twice the velocity of another would leave an indentation four times as deep, that three times the velocity yielded nine times the depth, and so on. [1] The adjacent device, shown at the Boerhaave Museum, Leiden, Netherlands, seems to be Gravesande's brass ball rolling clay surface experimental device. [3]

Gravesand shared these results with French mathematical physicist Emilie Chatelet, and with Voltaire (Chatelet's companion), after which, it is said, that Chatelet subsequently corrected English physicist Isaac Newton's formula E = mv to E = mv², and thus synthesized the first version of the conservation of energy (vis viva into vis mortua). This was a precursor step in the later 1905 derivation of the mass-energy equivalence formula of E = mc² by German-born American Albert Einstein. [2]


Left: four Leyden jars. Right: Dutch physical chemist Johannes van der Waals's energy surface for carbon dioxide. Both shown at the Boerhaave Museum, Leiden.

Ball and ring experiment
In circa 1720, Dutch physicist-mathematician Willem Gravesande invented the "ball and ring experiment" top demonstrate Boerhaave's law of volume expansion by heat, a rendition of which is shown above.

Leiden jar
In 1745, the Leyden jar, a an early type of capacitor for storing charge, was invented independently by German cleric Ewald Georg von Kleist, on October 11th, and by Dutch scientist Pieter van Musschenbroek of Leiden (Leyden), in 1745–1746. The invention was named for the city. The adjacent photo shows a set of four Leyden jars at the Boeraave Museum, Leiden. [3]

Energy surface for carbon dioxide

See also: Maxwell's thermodynamic surface

In circa 1890, Dutch physical chemist Johannes van der Waals published a treatise on the Theory of Binary Solutions in the Archives Néerlandaises, wherein he related his equation of state (see: Van der waals equation) with the second law of thermodynamics, in the form first proposed by American engineer Willard Gibbs, and was able to arrive at a graphical representation of his mathematical formulations in the form of a surface which he called Ψ (Psi) surface following Gibbs, who used the Greek letter Ψ for the free energy of a system with different phases in equilibrium. Shown adjacent is his energy surface for carbon dioxide, shown at the Boerhaave Museum, Leiden. [3]

Other alumni
The following are notables associated with Leiden University:

● Heike Kamerlingh-Onnes
● Jacobus van’t Hoff
● Bakhuis Roozeboom (1878)

References
1. Read, John. (1957). From Alchemy to Chemistry (pg. 124). Courier Dover Publications.
2. Bodanis, David. (2000). E = mc² - A Biography of the World's Most Famous Equation (pgs. 65, 68). Berkley Books.
3. Museum Boerhaave – Wikipedia.