during the Collapse of a Spherical Cavity. 97 



the pressure at any internal point. The general equation of 



pressure is 



1 dp Dw _ _ du du / Q v 



}dr~~"" 1 Dt~ ~dt~~ U dr> ' ' ' W 



u being a function o£ r and t, reckoned positive in the direction 

 of increasing r. As in (1), u = TJW/r 2 , and 



J4.W 



Also 



at dt dt at 



and by (4) 

 so that 



S " " p R 4 ' 

 ^(U 2 R)_ 9pn2 PR 3 



Thus, suitably determining the constant of integration, we get 

 p_ R |R 3 _ 4 1_R^ W_ x l (10) 



At the first moment after release, when R = R , we have 



p=P(l-R/r) (il) 



When r=R, that is on the boundary, p = Q, whatever R may 

 be, in accordance with assumptions already made. 



Initially the maximum p is at infinity, but as the con- 

 traction proceeds, this ceases to be true. If we introduce z 

 as before to represent R 3 /R 3 , (10) may be written 



|-l=-g(,-4)-g(,-l), . . . (12) 



The maximum value of p occurs when 

 r 3 4^—4 



(14) 



R 3 Z-4: ' 



and then 



p (*-4)B (z-i)* 



p- 1+ ^^-- 1+ 4:i(z-l)i ' ■ (15) 



Phil. Mag. S. 6. Vol. 34. No. 200. Aug. 1917. H 



