7 6 4 



B1RKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, 1902 1903. 



. f cos 8 cos cos /J 

 sin 2 // 



m 



ip \ Q L 



[am?** -j 



L cos ft d L 

 cos p 



_ . . f cos 6 cos t cos jff Q cos jj -\- d L 



2 



sin 



,"1 



Further we have 



Now 



therefore 



as 



Thus we find that 



f 



J 



Q.d 



f / f e cos /? + d - L . \ \ Q cos H + d - L , 



-tyr 1 - dQ \ dQ = Q \ - - dQ - 



J\J Q\ Q . d I J (>}Q.d 



rt \ it * n 



cos /? + d L , 



2 d 



= 



.. dL Z(Q - L cosfi} 



Iim = -- = Imi = - 



V? rf 



ail 



a o 



w 



Q cos ft -\~ d Z, 



e 



if ; /? 



J VP- 



We therefore put 



and obtain 



_ fa 



ir , TD\ JC V^ d i I cos co 

 F,(/?)= - -j- ^- 



'- ft i j sin*' 



Z. COS (S -f- Q 



~Z 



cos cos 8 

 -^ 



n 



i-j 



(22! 



where </ w is </'s value for Q = R . 



Here /i and J t are elliptic integrals. If, in the numerical calculation, the employment of LEGENI 

 tables is desired, they must be put into LEGENDRE'S normal form. If this is done by known method! 

 we find, if cp is introduced as a new variable determined by the equation 



