84 ON MAGNETISM. 



the needle is so turned that the edge of the needle is 

 reversed in regard to up and down. G is the place of 

 the center of gravity, whose longitudinal and transversal 

 ordinates will be called I and t. Put W for the weight of 

 the needle. Let H and V be the horizontal and vertical 

 terrestrial magnetic forces which act on each pole of the 

 needle before reversion of its magnetism : pulling the 

 red or lower pole, horizontally in the plane of vibration, 

 and downwards, respectively ; and pulling the blue or 

 upper end in the opposite directions : and let nH and 

 n V be the similar forces after the reversion of the poles. 

 (This amounts to the same as supposing that the mag- 

 netic intensity after reversion is to that before reversion 

 as n to 1.) Let a be the distance of each of the poles 

 from the center. Our object now is to find the propor- 

 tion of H to F. 



In Figures 31, 32, 33, 34, let V O y 6 9 0^ be the 

 angles made with the horizon by the line joining the 

 poles of the needles, which angle in each case may be 

 called the apparent dip. 



Then in Figure 31 the equation of equilibrium 

 will be 



TFx (Zcosflj + Jsintfj) + 2 Va cos X - 2Ha sin l = ; 

 or TFx (Zcot0 1 + ) + 2Facot0 1 -25a = 0. 



Similarly, 



inFigure32, TFx (7cot 2 -Q + 2Facot 2 - 2Ta=0; 

 in Figure 33, TFx ( - 1 cot 3 -t) + 2n Facot 8 - 2nHa=Q ; 

 in Figure 34, TFx ( - 1 cot 4 +*) + 2n Fa cot 4 -2ri5a=0. 



