820 

 Chemistry. — "In-, nmno- imd (liiyirlnnt i-iiuIUIii-'ki." . III. By Prof. 



SCHREINKMAKERS. 



(Communicaled in the meeting of October 30, 1915). 



(Jorrection. 



In the previous comrauiiii'ation II, the fio;iires 4 and 6, as will 

 have l)een oin'ious to the reader, have to he changed mutually. 



6. Quaternary sijstenis. 



In an invariant point of a quaternary system six phases occur, 

 which we shall call A, B, (J, D, EandF; consequently this point is 

 a sextuplepoint. Six curves start from this point, therefore; in 

 accordance with our previous notation we ought to call them 

 (A), {B), . . . . (F) ; here, however we shall represent them by yl', 5', 

 C' , D' , E' and F' . Further we find i (?z + 2) (n + 1) = 15 hivariant 

 regions. 



When we call the components A',, K,, K, and A'^ and when we 

 represent them by the anglepoints of a regidar tetrahedron, then 

 we are able to represent each phase, which contains these four 

 components, by a point in the space. As in a sextuplepoint six 

 phases occur, consequently we have to consider six points in the 

 space and their position with respect to one another. 



In general this representation in space can lead to difficulties for 

 the application to definite cases ; for this reason we shall later indi- 

 cate a method, which leads easily towards the purpose in every 

 definite case. Here, however, we shall use the representation in 

 space in order to deduce the different types of the possible P.T- 

 diagrams. 



When we consider the six points in the space, then they may 

 be situaled with respect to one another as in the figs. 1, 3, 5, and 7; 



In tigs. 1 and 3 they form the anglepoints of an octohedron, viz. 

 of a solid which is limited by eight triangles. In each of these 

 octohedrons we find twelve sides and three diagonals. [In fig. 1 AF, 

 EC and BD are the diagonals, in fig. 3 AF, EC and EF]. In 

 fig. 1 we find in each anglepoint four sides and one diagonal, in 

 fig. 3 we find in the anglepoints E and F three sides and two 

 diagonals, in the anglepoints A and C four sides and one diagonal 

 and in ihe anglepoints B and D five sides only. As in fig. 1 the 

 partition of the sides and the diagonals is a symmetrical one and, 

 however, in fig. 3 an asymmetrical one, we shall call lig. 1 asym- 

 metrical, fig. 3 an asymmetrical octohedron. 



