90 



while on the right we have 



„ P(a) -Rx, &(») - P^J 



where ft^ is the density at Infinity. The second term is 

 negligible for all stages of the motion except those 

 iiranediately following the explosion, so we may write (19) 

 in integrated form as 



2, / da 



^ /dal f 1 . 4 ^ 



--t^ ^(l" ^ 2a-da (20) 



The equvtion (20) is the extension of the energy equation (5) 



of Section 3 » to w'nlch it reduces as c — ><>=' , 



The factor (l " ■! -^-) on the left of (20) has 



•inerely the effect of making the curve of a against t 



asyauaetrical 'i.e., of nakinc the contrfiction slower than the 



expansion), v^ithout however producing any disaipation of 



enercy. Since ,^ ^ c for all those stages of the notion 

 ox 



which v,-0 are considering here, this factor is rather unim- 

 portant. The dissipation of energj"- arises from the term 

 dT 



in 5H on the right. For v;e have 



^ / — 



/•a /a- a 



/ -^ 





dr) 



Since 3^ *\ » this term is negative end beconies ever 

 greater in magnitude in the course of time. The effect of 

 this dlaElpat-.ion on the motion is discussed briefly in 



