394 



./ W. Gibbs on a Representation by Surfaces 



The relations of these lines and surfaces are roughly represented in 

 horizontal projection* in figure 2, in which the full lines represent 

 lines on the primitive surface, and the dotted lines those on the 

 derived surface. S, L, and V are the points which have a common 

 tangent plane and represent the states of solid, liquid, and vapor 



Fig. 2. 

 C 



which can exist in contact. The plane triangle SLV is the derived 

 surface representing compounds of these states. LL' and W are 

 the pair of lines traced by the rolling double tangent plane, between 

 which lies the derived surface representing compounds of licpiid and 

 vapor. W" and SS" are another such pair, between \vhich lies the 

 derived surface representing compounds of vapor and solid. SS'" 

 and LL'" are the third pair, between which lies the derived surface 

 representing a compound of solid and licpiid. L"'LL', WV" and 

 S"SS'" are the boundaries of the surfaces which i-epresent respectively 

 the absolutely stable states of liquid, vapor, and solid. 



The geometrical expression of the results Avhich Dr. Andrews 

 (Phil. Trans., vol. 159, p. 575) has obtained by his experiments with 

 carbonic acid is that, in the case of this substance at least, the derived 

 surface which represents a compound of liquid and vapor is termina- 

 ted as follows : as the tangent plane rolls upon the primitive surface, 

 the two points of contact approach one another and finally fall 



* A horizontal projection of the thermodynamic surface is identical with the dia- 

 gram described on pages 330-338 of this volume, under the name of the volume- 

 entropy diagram. 



