Figure (26) depicts the solution graphically. 



SUMMARY REMARKS (Plane Approximation) 

 While the formulas (9) through (13) are convenient for hand computing, since no root 

 extraction is involved, the use of trigonometric tables may make it unsuitable for larger machine 

 coding and computation, and it may be better to use the algebraic solution, equation (3). If the 

 algebraic solution is to be used, the number of significant figures to be retained in the co- 

 efficients of the resulting quartic, equation (3), will have to be considered relative to the 

 number of significant figures required in the rectangular coordinates of the intersections points. 



If solutions only above the base line, F' F", are desired (see Figure 24), then in the 

 trigonometric solution, equations (9) — (13), 6 should be limited to 77 > ^ > a . 



Note that the parameters a and b of the two families of confocal hyperbolas are related to 

 the fundamental constants of a Loran line by the relations (2.1). 



108 



