|Maxwell's thermodynamic surface, at Cambridge University, with 2007 overlay annotation added on by American engineer Ronald Kriz. 
“Maxwell expressed his appreciation of Gibbs’ thermodynamic surface by constructing a model of it for water and sending a cast of it to Gibbs and included a fourteen-page discussion of Gibbs surface in the 1875 edition of his textbook.”
“It is impossible to describe this thermodynamic surface in detail without considerable prolixity and use of the notions and terms of higher geometry.”
|Scottish engineer James Thomson's 1871 thermodynamics surface model, on display at the Hunterian Museum and Art Gallery, University of Glasgow; possibly a precursor or influence to Maxwell's thermodynamic surface.
“Are the numerical results of your former experiments on CO2 published anywhere except in the Philosophical Transactions ? I have just finished a clay model of a fancy surface, showing the solid, liquid, and gaseous states, and the continuity of liquid and gaseous states. I am afraid that even CO2 would not make a very compact model if worked true to scale. But the data as to specific heat in the liquid and solid states are wanting, and also the latent heat of fusion and evaporation.”
“You will be gratified to hear that Prof. Maxwell has made a clay model of your thermodynamic surface wherein entropy, energy, and volume are the three coordinates, and is able to explain a great deal by it.”
“It will give me great pleasure to receive on the part of the Cavendish Laboratory a cast of your thermodynamic model with lines marked on it. We know have got an excellent case with a glass front containing an thermometer by II Gonfio (before 1640, Wollastons optical and thermal apparatus, and others, and we shall have a special place for models such as yours. I enclosed a rough sketch of the lines of Gibbs’ surface, co-ordinates volume [x], entropy [y], energy [z], in an imaginary substance in which the principle features of the substance can be represented on a convenient scale.”
"I think you know Prof. J. Willard Gibbs' graphical methods in thermodynamics. Last winter I made several attempts to model the surface which he suggests, in which the three coordinates are volume, entropy and energy. The numerical data about entropy can only be obtained by integration from data which are for most bodies very insufficient, and besides it would require a very unwieldy model to get all the features, say of CO2, well represented, so I made no attempt at accuracy, but modeled a fictitious substance, in which the volume is greater when solid than when liquid; and in which, as in water, the saturated vapor becomes superheated by compression. When I had at last got a plaster cast I drew on it lines of equal pressure and temperature, so as to get a rough motion of their forms. This I did by placing the model in sunlight, and tracing the curve when the rays just grazed the surface... I send you a sketch of these lines..."
|One of Maxwell’s thermodynamic surfaces at the National Museums Scotland. (Ѻ)
“Copies of this model were distributed by Maxwell evidently with a certain amount of playful mystery, for each recipient thought that he was the happiest possessor of (at most) three. The writer knows of at six at least, and possibly there are more.”
“The statue which Clerk Maxwell sent to Willard Gibbs was a statue of water.”
“There is no record of Maxwell’s having corresponded with Gibbs on this (or any other) occasion, although one would expect that his gift of the model of the thermodynamic surface would have been accompanied by a letter of transmittal. This was either lost in transit or mislaid by Gibbs, as no such letter is included in the volume of his correspondence assembled by his brother-in-law nor did Gibbs ever allude to it as far as is known.”
|Gibbs 1873 figure 1.
|July 8th, 1875 sketches by Maxwell of "Gibbs' thermodynamics surface", as he called it, on a volume, entropy, energy plot. 
“Gibbs wrote about his new method and described it mathematically, yet he made no effort to make a diagram of what was, apparently, clearly seen in his own mind’s eye. The new method and the difficulty in having to visualize such complex material resulted in little attention from Gibbs’ scientific colleagues, especially in the United States. Yet, when Maxwell read Gibbs’ papers in Britain, he immediately saw the power and the potential of the new graphical method and would spend an entire winter constructing a 3D clay model of a surface using Gibbs’ data.”
“These solid diagrams have played a great part in the elaborate studies of the continuity of gaseous and liquid states by Van der Waals and his pupils, of which we have recently witnessed the final triumph in the liquefaction of helium.”
Gibbs was said to have been flattered and pleased with the gift of the water sculpture from Maxwell. Owing to his typical modesty, however, when students asked about it is said that Gibbs told them it came from a “friend in England”, rather than make mention that it came from the famous James Maxwell.  The anecdote seems to have originated from American writer Muriel Rukeyser's 1942 biography on Gibbs, where she states that the student was the father of a "Leonard Bacon". See main: Thermodynamics anecdotes
|2005 commemorative Gibbs stamp, showing an overlay of figure 26d "thermodynamic surface" of Scottish physisict James Maxwell's 1875 Theory of Heat, based on Gibbs' two 1873 graphical thermodynamics papers.
|Maxwell's thermodynamic surface on display at the physics department at Yale University.