24 



Vi = - 



4(2 - 7ra + 7m^) 



ra-'D 



6 = 



210 



10 - 33ni + 28ni^ 



"o 



2m3(m 



- 1)=^D 







15 - 25ra 



- 70m^ + 



98m3 



s 



4m^ 



(m - D^D 







3(2 - 



8ra + 7m^) 





^ m*(ra - D^D 



;> [55] (contd.) 



where 



D = 5 - l6m + l4m^ 



LIMITATION OF RANGE OF a^ BY THE "NO -INFLECTION POINT" CONDITION 



Let us again assume the values of the geometrical parameters which 



were used to Illustrate the sixth-degree polynomial form, viz, m = 0.40, 



r = 0.50, r, =0.10, and C =0.65. When ra is substituted into the Formulas 

 1 p 



[55] for the coefficients in the seventh-degree polynomials [54], the follow- 

 ing values are obtained: 



^ 



/3^ = -14.2857 

 e = 20.668 



a^ = 43.75 



Cg = -87.5 



r, = -9.5238 



^ = -3.8752 63 = -51.67 



r, =6.25 



^Q = n.5079 



5 = 250 



D = 0.84 



Put y^ = f(x), and 



g(x) = 2r^S^(x) + 2r^S^(x) + CpV(x) + W(x) 



Then 



f (x) = a U(x) + g(x) 



[56] 



where U(x) and g(x) are given polynomials. 



