WILLARD GIBBS 349 



diagram, as in the indicator cards for testing the efficiency of 

 steam-engines. In this the pressure of a gas is measured on one 

 line and its volume on a line at right angles to the first. A point 

 upon this diagram gives the state of the gas in regard to pressure 

 and volume, a line represents any change of state, and the areas 

 included measure the amount of work done on it in producing the 

 change. But of course such a diagram on a plane surface in two 

 dimensions cannot always clearly show the effects of changes in 

 other physical properties, as, for example, temperature. For this 

 a solid model in three dimensions is necessary, and the direct 

 representation of more than three such variables is impossible 

 because we cannot geometrically construct models of more than 

 three dimensions. But Gibbs showed that by choosing volume, 

 energy and entropy as the three physical properties of a body to 

 be represented by the rectangular coordinates, a geometrical sur- 

 face is formed which gives a complete graphical representation 

 of all the relations between volume, temperature, pressure, energy 

 and entropy for all states of a body, whether single or a mixture 

 of different states. 



The value of such graphical methods lies in the fact that they 

 give at a glance a clear and definite conception of complex rela- 

 tions, such as cannot be obtained, at least by the ordinary mind, 

 from the study of a table of figures or an algebraic formula. A 

 mass of experimental data, very incomprehensible in themselves 

 and even apparently improbable becomes quite clear on being 

 plotted upon a diagram, and new points of interest become ap- 

 parent, and promising lines of research are suggested. The use 

 of geometrical representations, many of which originated with 

 Gibbs, has been of great value in the development of the science 

 of physical chemistry. 



American scientists took little notice of " Gibbs' thermodynami- 

 cal surface" as it is called, but in England it attracted the attention 

 of Clerk Maxwell who in his Theory of Heat devotes considera- 

 ble space to it, and constructed with his own hands a plaster of 

 Paris model of such a surface for water in its three states of ice, 

 liquid and vapor. A cast of this was sent to Gibbs, who was much 



