we find from (157) that 



d = (0.97051129) (1.367673822 + 2.73347 x lO"* - 3.44 x IQ"') 

 d = (0.97051129) (1.36794682) = 1.327607833 

 X = (0.276886675) (0.994162934) = 0.27527047 



Y = 0.161262981 - 9.42015 x lO'" - 2.0700 x lO"' + 8.68 x 10"' = 0.16030113. 

 From(155). X = 0.27527045, Y = 0.16030112, and from Figure 22, d = 1.327607832. 

 Comparing with (159) we have a difference in d of 1 in the 9th decimal place; in X and Y 

 of 2 and 1 in the 8th decimal place respectively, which is within the computational 

 uncertainties. 



From (152), (153), (154), and (157) we can express the differences as functions of either 

 set of variables: 



Ad = d '- d = - (f/2) Y sin d + (fVl6) [4Y (X - 3) sin d + (2Y=' - X') sin 2d] , 



= -(f/2) Y'sind'-(fVl6) [4Y'(X'-l)sind'+(2Y'='-X'') sin 2d']; 

 AX = X '- X = fX(2 - X) il + (f/2) (3 - 2X)S , 



= fX'(2-X') ll-(f/2)(l-2X') }; 



AY = Y'-Y = fY(2-X) + (f/2) (X'-Y^) cos d 

 + (fV8) r 4Y (2 - X) (3 - 2X) 



+ (X' - Y' ) i (11 - 5X) cos d + Y (1 - 3 cosM) 

 = fY'(2-X') + (f/2)(X''- Y'^) cos d' 



(159) 



- (fV8) 



4Y'(2-X') (1-2X0 



+ (X"-Y'') !2(5-3X') cos d'+ Y'(l-3cosM') 



SUMMARY OF DISTANCE COMPUTATIONS INVESTIGATION 

 As long as accuracy requirements remain within the range of the capabilities of the 

 Andoyer-Lambert formulae, as exhibited in TABLE 3, they are quite adequate and it makes 

 no difference if geographic latitudes are transformed to parametric latitudes first as far as 

 accuracy requirements are concerned relative to hyperbolic electronic measuring systems. 

 However, the formulae for geodetic azimuths are slightly more complicated in terms of 

 geodetic latitude and some of the auxiliary quantities as chord length, dip of the chord, etc. 

 are slightly less difficult to compute when expressed in terms of parametric latitude. 



In order to arrange the computing in conformance with the Andoyer-Lambert formulae, 

 equations (17), (48), (52), 56)), and (64) have been rearranged as follows to be expressible 

 in common computational parameters: 



(160) 



93 



