821 



In fig. 5 five points tbnn tlie anglepoinls of a hexaliedron 

 within which the point F is sitnated. Wlien we omit the side-plane 

 BCD and when we unite F with B, 6', and D, then again an 

 octohedron arises, which we shall call nionoconcave. 



In fig. 7 fonr of the points form the anglepoints of a tetra- 

 hedron, within which the points E and F^ are situated. When 

 we unite E with the points A, B and D, the point E with (\ B 

 and D, and when we omit the side-planes ABD and CBD, then 

 a biconca\e octohedron arises. 



Type I. We shall deduce now the /^, 7'- diagram, when the six 

 phases form the anglepoints of a symmetrical octohedron (tig. 1). 

 We may consider this solid as construed of the four tetrahedrons 

 CABD, EABD, FBCl) and EBED, which terminate all in the 

 side BD. 



In order to determine the reaction between the phases of tlic 

 monovariant equilibrium F' , we consider the hexahedron CADBE; 

 as the diagonal CE intersects the triangle ABD, this leaction is: 

 C^ E^A + yi+ D 



Hence it follows : 



C' E' i E' I A' B' D' (1) 



In order to define the reaction between the phases of the mono- 

 variant equilibrium E' , we take the tetrahedron ACBDF; as the 

 diagonal /1 7'"' intersects the triangle BCJ), wo find for this reaction: 



/>'+ C-^ Dr^A^ F 

 Hence it follows: 



B' C' D' I E' i A' E' (2) 



We now draw in a P. 7'-d iagram (fig. 2) in any way the curves 

 E' and F' ; for fixing the ideas we draw E' at the left of/'"". [For 

 the definition of "at the left" and "at the right" of a curve we 

 have previously assumed that we find ourselves in the invariant 

 point on this curve, facing the stable part]. In accordance with this 

 assumption (1) and (2) have been written also at once in such a 

 way that herein É' is situated at the left of F' . 



It now follows from (1) and (2) that C' is situated at the left of 

 F' and E' \ C" is situated, therefore, as has also been drawn in fig. 2, 

 between the stable part of E' and the metastable part of F^' . 



Further it follows from (1) and (2) that the curves B' and D' 

 are situated at the right of F^' and at the left of E' ; they must, 

 therefore, as is also drawn in fig. 2, be situated between the meta- 

 stable parts of the curves E' and F' . The position of B' and D' 



