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MAGNETIC INCLINATION AT GOTTINGEN. 647 
asin (f+ g') sin (2¢ + f—g)=sin (f+ g).sin(2¢+/'—g'), 
whereby c is best determined by means of formula (9.), 
tan (2¢ —3(9 + o' —f—S)) 
sin —sin (/f! f 
~Xsin aan sin & = an er ad oP 
It further follows from (1.) and (2.), that 
2 cosi.sin(f + c)sin(g — c) — sinz. sin (f + g) 
= 2 alin PS er 
— 208 (@ aye 
thus by combination with (7.), 
sin (f+ 9) 
sin(2e +f— g) 
_ 2sin 4 sou c).sin(g — ¢) 
sin (2¢ + f—g) 
We deduce in a similar manner from (4.), (5.) and (8.), 
7 I U 
cotan (Q — c) = Gee oh 
2 sin (f" + c).sin(g’ — c) 
sin (2c +f! — g') 
If we write for the sake of brevity, 
cotan (f+c)=F cotan (f/f! + c) = F’ 
cotan (g—c) =G cotan (g! —c) = G, 
these two equations receive the form 
oni tan2 — saath 
G-—F G-—F 
cotan (Q— ¢) = . tani 
tan z 
cotan (Q — ¢c) = 
cotan (Q — c) = 
whence, lastly, we obtain ) 
G’—F’-G+F 
cotan (Q — c) = 
After i and Q have been found, ji may be determined from 
any one of the equations (1.), (2.), (4.), (5.), (7+), (8.)- 
In our example we have 
5: 587416)? 
583555) ° 
