ifi dlfferejM Latitudes. 



M" M' N' of a great circle, which when produced cuts the equa- 

 tor somewhere in N', at a distance from tlie point A, equal to 

 AN' or X, and under an inclination M'N' E', which I designate 

 by i ; then the two spheric triangles M' N' E', M" N' E" right 

 angled at E' and E", give these two equations, 

 tail? x' , ^ . tanp >." 



tang t = — " ~ 



tan; 



and tan'T i = —- ,,„ 



" sin .1/ —)/) 



r x" fii"n ;' -tans:x' sin /" 



from which we 



ein {i'- 



obtain tang x = „ , , „ ■ 



* tiing ;>." COS i'— tan^ X' cos (" 



This equation will determine x; that is the longitude of the 

 node of the great circle from any fixed meridian A .M, and the 

 other will determine M' N'E', or the inclination of the magnetic 

 equator* to the terrestrial eciuator. Nou', if all the observations 

 made in different parts of the world, when combined two and 

 two, give nearly the same values always for x and /', we may 

 conclude that the magnetic equator is a great circle of the ter- 

 restrial globe, at least in the extent embraced by the observa- 

 tions which we have used. To show how far this indication is 

 satisfactory, I have computed the following table : 



* This exprrssion for the tang x is not very convenient for comjiutinjj 

 by lojjuritliiiis; it would be better thus: 



/// x_ tangx' sin {i "-i') 



°^ ■'; tang x" -tang /.' cos (t"-0 ' 

 after which, taking un auxiliary anji+e ^, such that 



tang x' sin (/"— i') 



tang « = ,, ; 



^ ^ tang X" 



v,c shall find by eliminating tang x", 



sin {l"-i') fin ip 

 tang (t — .r) = — -. — — ; — j 



Tlic above t.iblc lias been computed by these formula;. 



The 



