(jJ, we thus have 



~E{c,90 o -p')+b*¥(c,90°-p')}; 



on an Oblate Spheroid. 335 



consequently positive ; that is. A, the longitude of the node, is 

 less than 90°, as it should be. Hence in order that A may be 

 = 90°, we must have V negative, say, A/ = — ///, where y! is po- 

 sitive ; and, observing that we may under the signs E, F write 

 90° -/n' instead of 90 c 



7T 7T - . 



.2=2 +e !vl-c 2 cosVtau/i' 

 that is, we must have 



tan/^Vl-^cosV^c, 90°- fM ! )-b 2 F(c } 90°-///); 

 viz. fjJ is here the parametric latitude (south) of the intersection 

 of the meridian C B with the consecutive geodesic line — that is, of 

 the point y. As /jJ increases from to 90°, the left-hand side 

 increases from to oo ; and the right-hand side, beginning from 

 a positive value and either attaining a maximum or not, ulti- 

 mately decreases to ; there is consequently a real root, which is 

 easily found by trial. 



C - 



Thus T== i, C = 4\/3 (the angle of modulus =60°), b = \; 

 A 



or the equation is 



tan^v / l-|cosV , =E(90 o -/^ , )-ii , (90°- A 6')- 

 Using Legend re's Table IX., we have 



/x'. 



90° -fx'. 



E. 



F. 



E-!F. 





tan/x'Vl — f cos 2 /x'. 



o 







o 



90 



1-21105 



2-15651 



•6719 



•o 



10 



80 



1-12248 



1-81252 



•6693 





20 



70 



1-02663 



1-49441 



•6530 





30 



60 



•91839 



1-21253 



•6153 



•3819 



40 



50 



•79538 



•96465 



•5542 



•6278 



so that we see the required value is between 30° and 40°; and 

 a rough interpolation gives the value yu/ = 37° 40'. But repeat- 

 ing the calculation with the values 37° and 38°, we have 



o 



37 



38 



90° -ju/. 



E. 



F. 



E-iF. 





tan fi'vl-| cos' 2 /x '. 



o 



53 

 52 



•833879 

 •821197 



1-035870 

 1-011849 



•57419 

 •56823 



•54425 

 •57108 



whence, interpolating, jjJ = S7° 55'. 



The semiaxes of the geodesic evolute, measured according to 

 their longitude and parametric latitude respectively, are thusBa, 



