88 



F. H. Bigeloio — Solution of the Aurora Problem. 



sin/sin(A + B) — A A, 

 cos £cos w = Ah. 



tan I sin (A + B) see w = 



AA 



^Ah 



Since the left hand number of this equation is derived from 

 theory, with the help of one assumed angle, and the right 

 hand member comes from observation, we have a test of the 

 correctness of our assumed angle. By trial and error, or 

 using this as an equation of condition, we can arrive at the 

 true angles involved. 



Fig. 3. — Showing the projection of the ray upon the reference plane. 



We have now found the true value of r', d\ for a point C on 

 the ray, and hence the order, IS 1 ", is given by 



8tt Bin 9 fl ' 



T' ~7~' 



Then we may change from r' to r = 1, at the surface of the 

 ground, and get the angular distance of 6 from the magnetic 

 pole, by 



sm o = — . 



For the height of C above the ground, we take r'—r cos (#' — #), 

 measured on the radius r' . 



