27 



By assuming other values for a^ it is now possible to obtain new 

 forms having the same values of the primary geometrical quantities m, r^, r^, 

 and C . The ranee of choice of a is limited, however, when inflection points 



P 2 



on the body are not permitted. With the values of m, r^, r^ , and C as 

 above, it was shown in the previous section that a is restricted to the range 

 -2 g a g 6. Forms corresponding to values of a^ near the limits of this 

 range, a = -1 , and a =5, are shown in Figure 6, together with the original 

 sixth-degree polynomial. It is seen that there is appreciable variation be- 

 tween these forms. It must be concluded that the geometrical parameters m, 

 r , r , and C alone do not suffice to fix a form. 



1 p 



From a practical point of view, however, the useable forms generated 

 by polynomials of the seventh degree can be fitted so closely by polynomials 

 of the sixth degree that no essentially new forms are introduced by the in- 

 crease in the number of degrees of freedom. As an illustration of this the 

 seventh-degree polynomials shown in Figure 6 have been fitted by sixth-degree 

 polynomials by the method of least squares, and, as is shown in Figures 7 and 

 8, the fits obtained are excellent. The method of curve fitting employed 

 here Is described in Appendix 4. 



It is further believed that practically all streamlined forms satis- 

 fying the no-inflection-point condition can be well-fitted by sixth-degree 

 polynomial forms. From this point of view, although the parameters m, r^, r , 

 and C alone do not suffice to fix a form, by their variation they determine 

 all the desirable forms generated by sixth-degree polynomials, and thus, in 

 the above sense, all the desirable stream forms. 



