827 



Now it follows from (13) and (14) that the bundle of the curves 

 A', B' , C' and D' must be situated at the right of F' and at the 

 left of E' ; tlierefore, these curves are situated, as is also drawn in 

 fig. 8, within the angle, which is formed by the metastable parts 

 of E' and F' . 



Now we have still to define the position of those four curves witli 

 respect to one anotiier. As the five phases of the equilibrium A' 

 form a tetrahedron EBCD, within which the point F is situated, 

 we find : 



F' I .1"! B'C'D'E' (151 



Hence it follows tiiat curve A' must be situated as is drawn in 

 the figure. 



The five pliases of tiie equilibrium 6" form the tetrahedron i*'J/ii>, 

 within which the point E; lience it follows: 



E' i C' I A'B'D'F' (16) 



Hence it is apparent tiiat curve 6" must be situated as is drawn 

 in the figure. 



Ijater we shall define tiie position of the curves B' and D' with 

 respect to one another. 



We have found the following above: 



when the six phases form tiie anglepoints of a biconcave octohedron. 

 then the six nionovariant curves form in the i-',7'-diagram one 

 fourcurvical and two onecurvical bundles. 



Though we have deduced the four types of the y-*, ^'-diagrams 

 without knowing the position of the curves B' and D' with respect 

 to one another, yet we shall define the position of the curves B' 

 and D' with respect to one another. For this we have to consider 

 the position of the five phases of each of the equilibria B' and D' . 



For this we consider the line AI^ ; this line intersects in each of 

 the solids (ligs. 1, 3, 5 and 7) either the triangle iJC'^ or the triangle 

 DCE. Now we assume that it intersects in each of these solids the 

 triangle BCE. 



As the [\vë pliases of tlie equilibrium D' form the hexahedron 



ACEBF, the diagonal of which intersects the triangle CEB, it follows : 



A'F' I D' I B'C'E' (17) 



The five phases of the equilibrium B' form the anglepoints of 

 the hexahedron ACDEF. As, in accordance with our assumption 

 the line AF does not intersect the triangle CDE, the line CE will 

 intersect the triangle AFD. Hence it follows: 



A'D'F' I B' I CE' , fl8) 



It is apparent from (J 7) that in each of the figures 2, 4, 6 and 



