ACTION OF A MAGNET ON A COMPASS NEEDLE. 127 



this is greatest when tan < = 2, which gives the depres- 

 sion of the center of the magnet below the compass 

 h 



54. The disturbing magnet is in the horizontal plane 

 which passes through the compass, but is inclined at any 

 angle to the line joining the centers of the magnets. 



In Figure 44, it will readily be 

 seen that the resolved part of the 

 force in the direction of c is 



a . (c a cos 6) (c 2 2ca cos 6 + a 2 )"^ 

 - a . (c + a cos 6) (c 2 + 2ca cos 6 + a 2 )"^ : 

 and the resolved part perpendicular 

 to c towards the right is 



a . a sin 0(c 2 - 2ca cos + a 2 )" 1 



+ a . a sin 0(c 2 + 2ca cos 6 + a 2 )'^. 



If we expand these to the third power of - , we find, 



c 



Force in the direction of c 



= ^cos 6 jl + ^ (5 cos 2 6 - 3) i ; 



Force transversal to c 



a 2 / 15 

 7 2 V2 



The square root of the sum of the squares of these will 

 give the whole force on the red end of the compass- 



