6 14 MAGNETIC FIELD. 



2 



Observing that tan I' = - t and dividing the several terms of this 

 H 



equation by the former, we get, to the same degree of approximation, 





or, if q is the coefficient of variation of the product Q with the 

 temperature, 



The principal factor (cot /3 + cot I'), by which we should multiply the 

 angular variation observed dO t will be determined by experiment. 



If the axis of rotation is perpendicular to* the meridian, I' = I ; 

 if it is parallel to the meridian, cotl' = 0. In this latter case, the 

 formula is more simple ; but the action of the earth tends to turn 

 the knife-edge on the planes, and the course of the instrument may 

 be less regular. 



In the general case, the couple which tends to bring the bar 

 to its position of equilibrium, when once it is deflected by a small 

 angle 8, is 



[Q cos (P + 0) + H'M cos 6 + ZM sin 0] 8 , 



an expression which, when the angle is very small, may be 

 reduced to 



(Qcos/3 + H'M)S. 



If then we make the balance oscillate in the meridian, and then 

 in a plane perpendicular to this meridian, the corresponding numbers 

 of oscillations n and ri give 



_ HM 



Q cos ft ' 



As we have sensibly 



ZM = Qsin/3, 

 it follows that 



H n'* ri* 



cot/? = - - - = - - cot I. 



