4 i6 SCIENCE PROGRESS 



A transformation ' somewhat similar to (22) then leads to 



rift 



dt 



/*& + ?ft 



I 



and we have, in this case, 



(29) 



and 



2fxR 2 



(SO) 

 (SO 



(32) 



(33) 



The course of these integral curves is shown in figs. 4 and 5. 



Fig. 1. Roots \ real 

 and both ^ o. 

 Stability. 



Fig. 2. Roots X real 



and both )> o. 



Instability. 



Fig. 3. Roots X real and 



of opposite sign. 



Instability. 



Fig. 4. Roots X complex ; 

 fi <( o. Stability. 



P'ig. 5. Roots X complex ; 

 fi y o. Instability. 



Summary. — It has been pointed out by biologists that 

 organic evolution is an irreversible process. Physicists also 



1 See, for example, Liebmann, Lehrbuch der Differentialgleichungen, pp. 99, 



ML 



