150 Prof. A. M c Aulay on Spontaneous Generation 



matical interpretations. This approximate identity of results, 

 for our purposes, is probably due to the third order terms of 

 to in both cases being a multiple of the discriminant of 

 X + km 1 where k is a constant. 



efg is not a rational function of s\ s", and s' /; , and we 

 naturally take efg really to be merely the third order term 

 of some function of third and higher orders. This generalized 

 form of efg need not go beyond the fifth order, since 



s "> + s ' s "= - iefy + 1-2 [e* + 6/y - ie 3 (f+ff) - IWfg] 



but it is simplest to let it go to the sixth order by generalizing 

 efg to 



«/&(i+W(i+w(i+fe)=^fi6r,si;&i)65r8] 



=*Sf 1 &f i Si;Siii6wt 8 + iSei« U (56) 



= m'"(l + W + im" + X') + iSeue. J 



The last transformation follows by noting that since 

 v =(l + 2%0%5 the discriminant of v is the product of the 

 discriminants of l + £%' and %. If we neglect terms above 

 the third order (56) reduces to 



efg=m»' + i8€ X 6 (57) 



Consistently with the above, and initially making no 

 assumption that rj is small, put 



iv/B = l%W- (l-Jfe)EFG— (1/8/) (E 2 -l) (F 2 - 1) (G 2 -l) 



. . . (58) 



where B, k, and I are given constants. 



To get stationary values of id equate to E , &c v to zero. 



E_(1~/:)FG-(1/4Z)E(F 2 -1)(G 2 -1) = 0. 

 Multiply by E and write the next similar equation. 



E^(l-^)EFG-(1/40E 2 (F 2 -1)(G 2 ~1) = 0, 

 F 2 ~(1-AOEFG-(1/4Z)F 2 (G 2 -1)(E 2 -1) = 0. 

 Subtract and reject the factor E + F. 



(E-F)[l+(G 2 -l)/l/]=0. 

 Similarly 



(F-G)[l + (E 2 -l)/4/]=0. 



