88 ON MAGNETISM. 



of which the sum is 



- + a + 4 



cot l + cot 2 cot 3 + cot 6 



whence 



TV F_ 2 / 1 

 Jlp ~ H~ 1 + 



If n has been numerically calculated, from the for- 

 mula above, the computation of tan . Dip may most 

 readily be made by substituting the numerical value in 

 this expression. Or, if the symbolical expression for n 

 be substituted, 



tan . Dip 



__ 2(cot0 8 -cot0 1 +cot0 a -cot0 4 ) _ 



In ordinary observations with the dipping-needle, 

 these formulae are not required. But they are required 

 in the following case. The adjustment of the instru- 

 ment which it is peculiarly beyond the power of the 

 observer to verify, is the circularity of the pivots. Some 

 observers therefore have thought it desirable that the 

 needle should be so unequally loaded as to be sensibly 

 out of balance, thus making the apparent dips t , 2 , 6 y 

 4 very unequal, and bringing different sides of the 

 pivot into bearing upon its agate edges. With that 

 arrangement, the formulas above investigated are ne- 

 cessary. 



40. Theory of the Dipping-Needle when the dips 

 are observed in different vertical planes inclined to the 

 plane of the magnetic meridian. 



