56 



i(x) = c(- 



T" 



where 



and 



+ a x + a x 



a a„ a. 



•) 



C = 4T + -2 + T log 4 ) 

 m(a) =±y Ca 2 y^a^ 



/ 



The expression for m(x) in [135] may also be written as 



i(x) = c(-^+ y 2 ) 



[135] 



J36] 



[135a] 



When a < the solution for a in [13*0 indicates that there would 



3 



be no real roots near a = 4. In this case a graph of the complete polynomial 

 in [125] should be examined either for the possibility that more complete cal- 

 culations would show that there are real roots near a = 4 nevertheless, or 

 that the maximum value of the complete polynomial in the neighborhood of a = 4 

 is so nearly zero, that the value of a corresponding to this maximum may be 

 taken as an approximate solution. On this assumption, the second order analy- 

 sis would give 



= 4 + a. 



a_ < 



:i37: 



Since a does not occur explicitly in Equations [135], it is seen that they 



3 



would also be obtained, to the same order of approximation, if the value of 

 a in [137] were substituted into Equations [126] through [129], 



If it is determined that not even an approximate solution can be 

 assumed near a = 4 it would be necessary to consider solutions in the neighbor- 

 hood of the other roots of Equation [131]. 



In order to facilitate the computations for graphing the polynomial 

 in [125], the functions A(a), B(a), ... H(a), where 



