78 





/ z ^ (1 - z) dz 



Bi. 

 L 



(l-l) - \ (I'D (^) 



where B-a.{M,n) s 



(1-x) dx is the inconplate beta 



(7) 



fiinctlon. Uov; in the range from to l/2 the factor 



-'A 



(1-z) varies quite slowly, and it can bo quite satis- 

 factorily approximated ever the range of intecratlon by 

 a parabola. By this means the curve shovm in Fig. 2 

 was constructed. Tlie radius-tino curve is thus 



v/here s is 0^"^®^^ tiy (5) and (3) and Bj, is to be read from 

 Pig. 5 . 



The period is obtained in the present approximation 

 by setting z s in (7) and multiplying; by tv/o. "vVe have 



„„ /5 5\ . „ f5 5^ » U (f)l 



so the period is 

 T 



s 1.135 ^'^v'J'" W ^^ 



(0) 



Let us now consider the otlier extrorie, that of 

 sr.iell oscillations about the equilibrium radius ^i . If 

 tho pre s sure -voluma relation for the c^s is 



pa 



- Poo ai 



i'i 



(9) 



