40 



this line continues to proceed to lower temperatures, and p continues 

 to rise to intinitelj great ; or tliat after liaving reached certain 

 minimum of temperature, it proceeds to higher temperatures, again 

 before p has become infinitely great. If tlie latter should be the 

 case there is in the p,T-\mQ of the coexistence a point in which 



(i Ï} 'ill 17 



-— = =00, or vi=:Vs. And for the points of the line of 



dT VI — Vg 



coexistence which lie higher, vi has then become ^ Vs, and the above 



described case occurs again. Nor is there a difference of significance 



when V always remains greater than vi. At the temperature of the 



disappearance of the solid state, which is then lower than the 



temperature of the triple point, this disappearance takes place at a 



pressure equal to infinity. Since, however, Va is always greater than 



vi, we can hardly continue to speak of "expelled". The volumes 



Vs and vi have now however both become ecpial to Vq, and on rise 



of the temperature it is again only the liquid which can exist. 



Assuming here again that liquids under a very high pressure, 

 and so in a very small volume, almost equal to Vo, assume the 

 viscous state, we might point out the following difference. If 

 i's<C^/ these substances have the solid state in volumes which are 

 little greater than r^ at temperatures somewhat below that of the 

 disappearance of the solid state ; they have the viscous state on 

 increase of volume, and on further increase of the volume they 

 have the liquid state. If on the other hand Vg'^vi, the succession 

 of the 2 solid states is reversed. 



At the highest temperature for the existence of the solid state 

 the difference between solid and viscous has probably disappeared 

 under infinite pressure. 



Physics. — "On a system of curves occurring in Einstein's theory 

 of gravitation". By Ch. H. van Os. (Communicated by Prof. 



H. A. LOKENTZ). 



In Prof. P. Ehkenfest's communication on Einstein's gravitation 

 theory (Vol. XV, p. 1187) a system of oc^ curves occurs which is 

 determined by the condition that a hyperboloid : 



H = A{x"- + y' - z') -t- Bx + Cy ^- Dz + E = 0, . . (1) 

 a so-called "light hyperboloid" can always be brought through two 

 of these curves. This system will be examined more closely here. 



The curves are intersections of the hyperboloids H. As they must 

 also have a conic /^oo 



