86 ON MAGNETISM. 



If the needle is very nearly balanced on its pivots 

 (a condition which the artist always endeavours to 

 secure), so that the four angles V 2 , 8 , 6^ are nearly 

 equal : then we have, without perceptible error, 



cot X + cot 2 = 2 cot * 2 ; cot 8 + cot 4 = 2 cot 3 4 ; 



I, . 



and tan . Dip = - \ tan -*-= 2 + tan 



0, 4- 2 + 19, -f 

 = tan - 1 - ^ 5 



(by the same reasoning as that just employed) : and 

 consequently 



39. Mathematical theory of the Dipping -Needle 

 continued : secondly, on the supposition that the intensity 

 is not the same after reversion, and that the needle is not 

 nearly balanced. 



We must now use the accurate equations near the 

 beginning of the last Article : and first, to find the 

 value of n. 



Multiply the first equation by tan t and the second 

 by tan a , and subtract ; 



Wt (tan t + tan 2 ) - ZHa (tan 0^- tan 2 ) = 0. 



Multiply the third equation by tan 3 and the fourth 

 by tan 4 and subtract ; 



Wt (tan 4 + tan 8 ) - 2nHa (tan 4 - tan 8 ) = 0. 



