150 Trans. Acad. Sci. of St. Louis. 



tating gaskugel, the pressure being due to the alleged at- 

 traction of this core for the superposed, layers. Equations 

 (3), (6) and (7), involve no such conditions. 



If we a.ssume that the mass 31 has initially a radius li,, 

 and that it contracts to a radius JR, so that Rg = pli, then 

 the two equations for P will be 



4 — 3n M^k 



P 



87rn RJ' 



4 — 3n M'^k 



Sttti i?« 



Hence 



P ~ \RJ 



or P^p*P„- (26a) 



In a .similar way it may be shown that 



S=p^8, (27) 



and T= —• ('^^) 



P 



In Ritter's well-known paper of 1878* he established the 

 relations involved in the last three equations, by an ingenious 

 train of reasoning. He assumes a gravitating weltkugel to 



so contract, that any and every linear distance has become — 



•' - m 



of its original value. Then the volume of unit mass at any 

 point, in terms of the initial volume, is 



By reason of this contraction, the gravitational pull on each 



* Annalen der Physik unci der Cheraie. B 1. V, 8. 549-50. 



