204 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
28 
If T*=o0 the validity of (43) depends on convergence of the 
integrals involved. 
One application of (43) will be used repeatedly. We define 
a bulge in a growth path (x,, z,) as an interval [T, T*] such that 
‘44, 
r 
(44a) o=T <T* <0, 252 25 = 2% say, and 
(446) either * < #() and 2, <z* for T<t < T* 
> 7(s) and 2,>=z* for T<t< T* 
where the definition (26) of 2(p) is extended to all values of o, 
( (154) A) =7 for psg) 
“ (450) g(2(e) = for g(3) <p < glo) 
(45¢) Zp)=o for g'(o)- 
4+| Koopmans - pag. 40