150 Trans. Acad. Set. 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 assume that the mass M has initially a radius i?„, 

 and that it contracts to a radius E, so that R„ = pB, then 

 the two equations for P will be 



4 — 3n ]\Pk 

 ^o "^ 87rn Bj 



4_3n M'^k 



87rn i?* 



Hence 



or 



P - \Ro' 

 P^pip^. (26a) 



In a similar way it may be shown that 



B = p'B, (27) 



and y= — . (2^> 



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 



1 

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



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 

 * Aaaalen der Physik und der Cht^mie. B\. V, 8. 549-50. 



