30 



AKSEL S. STEEN. 



M.-N. Kl. 



The arc of the great circle, b, between two places on the earth's 

 surface, whose geographical latitude, cp^ and (p^, and difference in longi- 

 tude, X, are known, is obtained by the following formula : 



cos b = cos T sin cp^ sin (p^ -\- cos (p^ cos rp^- (2) 



By the aid of these formulae, I have found the value of // for each 

 of the 4 points to be 



887 



703 

 1007 



A. 

 B. 

 C. 

 D. 



km. 



In order also to obtain some sort of idea as to how far north that 

 part of the current setting due west will be found, and at what height 

 above the earth it is at that place, I have reasoned as follows: 



The setting of the current direct from E to W means that J Y= o. 

 Calling that value of JX and of z/Z which answers to z/F=o, respec- 

 tively jXm and jZai, we may put 



jZa 



JX^ 



= tan t, 



where i denotes the angle which the deflecting force, at that moment lying 



n the meridian plane, makes with the horizon. 



Fig. 7 represents a meridian 

 section through the station a, which 

 has a latitude cp. Let us assume 

 that there is a current running 

 from E to W, that is, perpendicu- 

 lar to the plane of the paper 

 through point 5. This current will 

 produce the deflecting force aK, 

 which makes with the horizon the 

 angle i = the angle Saz. The 

 current is at an altitude /t above 

 the place M, whose latitude is ip. 

 Calling the earth's radius R, we 



Fig. 7. 



obtain the following equation: 



(R -j- /i) sin {z -\- q) — ip) = R sin t. (3) 



Thus for the determination of ip and /i, observations from at least 

 two stations with the same geographical longitude are required. 

 From Tables 2 and 3, we find, by graphic interpolation, 



