21 



TABLE 1 



ABSCISSAE AND WEIGHTING FACTORS FOR GAUSS' QUADRATURE FORMULA 



1 



n = 7 



n - 



= 11 



n = 16 



k 



R i 



«I 



R i 



*i 



R i 



1 



-0.949108 



0.129485 



-0.978229 



O.055669 



-0.989401 



0.027152 



2 



.7^1531 



.279705 



.887063 



.125580 



.944575 



.062254 



3 



-0.405845 



.381830 



.730152 



.186290 



.865631 



•095159 



4 







0.417959 



.519096 



.233194 



.755404 



.124629 



5 

 6 



*i = "^n-i+1 



R i = R n-i+l 



-0.2695^3 

 



.262805 

 O.272925 



.617876 

 .458017 



.149596 

 .169157 



7 



8 







*i = "*n-l+l 



R i = R n-i+1 



.281604 

 -0.095013 

 *i = "^n-i+1 



.182603 

 0.189451 



R i = R n-i+1 



ILLUSTRATIVE EXAMPLE 



The foregoing considerations will now be applied to a body of rev- 

 olution whose meridian profile is given, for -1 ^ x ^ 1 , by 



y 2 = f(x) = 0.04(1 - x 4 ) 



[78] 



The body is symmetric fore and aft, has a length-diameter ratio X = 5» and a 

 prismatic coefficient 



<j> = f (1 - x 4 )dx = 0.8 

 Jo 



By applying to [78] the transformation 



x = 2| - 1 , y = 277 



[79: 



We obtain the equation for the geometrically similar body of unit length, for 

 £* < 1, 



7] z = 0.08U - 3$ 2 + 4| 3 - 2£ 4 ) = 0.08^(1 - £)(2* 2 - 2* + 1) [81] 



