350 



which Is formula (1.11). The total period rrom beginning 

 to minimum will be twice t, . 



Momentum of the Bubble 



The vertical momentum, s, of the bubble is equal to 

 a d/3. Using the Lagrangian equation associated v/ith the 

 b coordinate, we find that 



(3.12) ^(aVs) = a^a^L ^ + a^z^^, 



Integration gives the value of s at the maximum as 



S3_t = 2[J ^ a^4^L -aF ^* ■*■ ^o""" / "^ ^^'^^'^ ' 

 o o 



Using equations (3.7) and (3.8) and the fact that 



adt = da 



we express s, as integrals over a. We have 



3^ = L ^ f^ a^/2(l.aL^,)-^/2l/l-a^-I.a-^(^-^)" da 



^o 



, oa, a^/^(l + a.L(p./2)da 

 (3.13) + zl / 



M^ /l - a^ - Vca-^(^-l)- 



^9^1 1 -11 



= ^ ^(^3 - i ^^^4) ^ ^o (I5 ^ ^ ^^'1^6^ 



where 



