Edinburgh born physicist James Clerk Maxwell created this 3D model to represent the behaviour of an imaginary substance showing its solid, liquid, and gas states.

Who was James Clerk Maxwell?

James Clerk Maxwell (1831-1879) was born in Edinburgh, and in his comparatively short life became one of the world’s greatest physicists. He studied at the Universities of Edinburgh and Cambridge, before holding a professorship at Marischal College in Aberdeen. Later he worked at King’s College London and Cambridge.

Maxwell is particularly acknowledged among scientists for combining the theories of electricity and magnetism into electromagnetism. However, his research was very wide ranging, as shown by the variety of objects in our collections.

What does this model show?

This model is a three dimensional graph. It represents the behaviour of an imaginary substance showing its solid, liquid, and gas states. The substance is like water, showing behaviours such as expanding as it freezes. But the model doesn’t use accurate data for water itself as this wouldn’t fit so conveniently into a compact 3D structure.

James Clerk Maxwell’s was not the first model of this type to be made showing the behaviour of materials. In 1862-71 in Belfast, James Thomson (whose more famous younger brother became Lord Kelvin) worked on data gathered by Thomas Andrews. He used this to make three-dimensional graphs showing the relationship between volume, temperature, and pressure of carbon dioxide, whether it was a gas or liquid. Maxwell was fully aware of their work and some interesting insights into the making of the model are found in letters between them.

How was the model made?

Maxwell’s model was based on equations by Josiah Gibbs (1839–1903). It demonstrated the volume, energy, and entropy of the substance. Maxwell sculpted the initial model in clay, which took several attempts. He then replicated it in plaster.

The lines on the surface of the model include lines of constant temperature (in red) and constant pressure (in blue). Some of these were drawn by Maxwell by placing the model at an angle in the sun and tracing the curve where the light rays grazed the surface.

How many of these models exist?

Maxwell sent one of his models to Gibbs in America, where it is preserved at Yale University together with some later copies of it. Another remains at the Cavendish Laboratory in Cambridge. He sent another to his correspondent Thomas Andrews in Belfast, and two examples are in the collections of National Museums Scotland.

One of the examples in our collections is the one Maxwell sent in 1878 to his life-long friend and Professor of Natural Philosophy at Edinburgh, Peter Guthrie Tait (1831–1901). Another example was given to his former student, George Chrystal (1851–1911) who in 1879 became Professor of Mathematics at Edinburgh. This example was passed by Chrystal’s family to the Chemistry Professor Alexander Crum Brown. He exhibited the model in a 1914 exhibition to celebrate the 300th anniversary of the discovery of Logarithms.

Both of these examples were preserved in the Natural Philosophy collection at the University of Edinburgh before coming to the Museum.

These five models were not the only ones Maxwell made. In a book review of Gibbs’ work there is reference to at least one more.

This review is signed only with the initials C.G.K., but was clearly written by Cargill Gilston Knott. At the time Knott was a Reader in Applied Mathematics at Edinburgh University and was presumably aware of the two Edinburgh examples.

Chrystal’s example of the thermodynamic surface (museum reference T.1999.301) is on display in the Enquire gallery at the National Museum of Scotland. It is shown alongside one of James Thomson’s models of carbon dioxide.