aEODESIC INVESTIGATIONS. 57 



FOEMULAE AREANG-ED FOE CALCULATIONS. 



For approximate values of I", w, and A". 



I ' (1— e- siu- i')"^ in whicli e is earth's excentricity. 



Ii2sinl" 2i2sinl" i '^ 



(? sin A' 



R cos ?" sin 1" 



A" -A'-w sin i (l" + 

 cos ^ {I" - I') 



For \', v', and approximate value of k" and i/". 



tan a' =; — tan I' 

 a' 



tan a" = — tan Z" approx. 

 a~ 



v' —l — K' 



v" = I" — a" approx. 



For the geocentric radii-rectors /, r" to stations. 



I cos a' cos y' J 



„ ( a- cos I" ) \ 



*■ = \ -77 T/ \ a-pprox. 



(. cos a" cos v" ) 



For the radii of curvature of the meridians at the stations. 



7?' — « ( 1 - g') 



(1 - e- sin 2 ?')! 



^„ a (1 — e'-) 



-^ — ri ■ %v' \^ approx. 



(1 — e- sin'' t ) 2 



For radii of curvature of arcs perpendicular to the meridians at the stations. 



R a ^ 



(1— e- sin- I ) 



R _ ff. , 



" '~ 0—e'sm'l"f approx. 



