( 424 ) 



by VAN DEI? Waals. The necessity of double retrograde condensation 

 (fourfold intersection wilh a line // t;-axis) is seen in figure D. 



In the second supposition (Figs. EC') 2 passes through the critical 

 end point {B') and immediately after we again obtain the configuration 

 which involves double retrograde condensation with this [)eculiarity 



I, 3 



B z 



d. x.c.jr 



however, that the first retrograde condensation which occurs on 

 compression is retrograde condensation "of the second kind" owing 

 to the position of the plaitpoint on the vapour side. The phenomenon 

 as a whole might therefore be called double retrograde condensation 

 of the .second kind. The maximum vapour pressure disappears inside 

 the triangle itself in consequence of the transformations which we 

 know from Korteweg's investigations take place inside the plait in 

 this case. Whether the first or the second supposition is the correct 

 one, say for ether and water, 1 shall not try to decide. 



Mathematics. — "The characteristic numbers of the pri.smotope." 

 By Prof. P. H. Schoute. 



1 . AJode of generation. Let S„^ , 6',,. , . . . , .S'„ represent a certain 



number p of spaces respectively of n^ , n^ , . . . , ?iy dimensions having 

 by two no point in common Imt the point O common to them all. 

 Jjet us assume in each of these spaces a definite polytope with 

 as one of its vertices, and let us denote the ])olytope in ;S„j by (P^„j , 

 that in S„^ by (P)„^ , . . . , that in ,S'„^ by (P)„ . Now let us move 



{P)n„, remaining equipollent to itself, in such a way that the point 

 coinciding originally with coincides successively with each point 

 within (P)„i; then the locus of all the positions of {P)n^_ is a pris- 

 motope with two constituents {P)^y , (P),!^ which may be represented 

 by the symbol {P^ ; I\.X Kow let us move (P),,, , remaining equi- 

 pollent to itself, in such a way that the point coinciding originally 

 with coincides successively with each point within ij\ ; I\) ; 

 then the locus of all the positions of (P)„3 is a prismotope with three 



